{"id":2849,"date":"2021-07-23T16:00:38","date_gmt":"2021-07-23T10:30:38","guid":{"rendered":"http:\/\/mcq-questions.com\/?p=2849"},"modified":"2022-03-02T10:23:19","modified_gmt":"2022-03-02T04:53:19","slug":"ncert-solutions-for-class-9-maths-chapter-8-hindi","status":"publish","type":"post","link":"https:\/\/mcq-questions.com\/ncert-solutions-for-class-9-maths-chapter-8-hindi\/","title":{"rendered":"NCERT Solutions for Class 9 Maths Chapter 8 Quadrilaterals (Hindi Medium)"},"content":{"rendered":"

NCERT Solutions for Class 9 Maths Chapter 8 Quadrilaterals (\u091a\u0924\u0941\u0930\u094d\u092d\u0941\u091c) (Hindi Medium)<\/span><\/h2>\n

These Solutions are part of NCERT Solutions for Class 9 Maths in Hindi Medium<\/a>. Here we have given NCERT Solutions for Class 9 Maths Chapter 8 Quadrilaterals.<\/p>\n

\u092a\u094d\u0930\u0936\u094d\u0928\u093e\u0935\u0932\u0940 8.1\u00a0<\/strong><\/span><\/p>\n

Ex 8.1 Class 9 \u0917\u0923\u093f\u0924 Q1. \u090f\u0915 \u091a\u0924\u0941\u0930\u094d\u092d\u0941\u091c \u0915\u0947 \u0915\u094b\u0923 3 : 5 : 9 : 13 \u0915\u0947 \u0905\u0928\u0941\u092a\u093e\u0924 \u092e\u0947\u0902 \u0939\u0948\u0902 | \u0907\u0938 \u091a\u0924\u0941\u0930\u094d\u092d\u0941\u091c \u0915\u0947 \u0938\u092d\u0940 \u0915\u094b\u0923 \u091c\u094d\u091e\u093e\u0924 \u0915\u0940\u091c\u093f\u090f |<\/strong>
\n\u0939\u0932 :<\/strong>
\n\"NCERT
\n\u092e\u093e\u0928\u093e \u2220A = 3x,
\n\u2220B = 5x,
\n\u2220C = 9x \u0914\u0930
\n\u2220D = 13x,
\n\u2234\u2220A + \u2220B + \u2220C + \u2220D = 360o<\/sup>
\n(\u0915\u093f\u0938\u0940 \u091a\u0924\u0941\u0930\u094d\u092d\u0941\u091c \u0915\u0947 \u091a\u093e\u0930\u094b\u0902 \u0915\u094b\u0923\u094b\u0902 \u0915\u093e \u092f\u094b\u0917 360\u0966<\/sup>\u00a0\u0939\u094b\u0924\u093e \u0939\u0948 )
\n\u21d2\u00a03x + 5x + 9x + 13x = 360o<\/sup>
\n\u21d2\u00a030x = 360o<\/sup>
\n\"NCERT
\n\u0905\u0924: \u0938\u092d\u0940 \u0915\u094b\u0923
\n\u2220A = 3x = 3 \u00d7 12o<\/sup>\u00a0= 36o<\/sup>
\n\u2220B = 5x = 5 \u00d7 12o<\/sup>\u00a0= 60o<\/sup>
\n\u2220C = 9x = 9 \u00d7 12o<\/sup>\u00a0= 108o<\/sup>
\n\u2220D = 13x = 13 \u00d7 12o<\/sup>\u00a0= 156o<\/sup>\u200b<\/p>\n

Ex 8.1 Class 9 \u0917\u0923\u093f\u0924\u00a0Q2. \u092f\u0926\u093f \u090f\u0915 \u0938\u092e\u093e\u0902\u0924\u0930 \u091a\u0924\u0941\u0930\u094d\u092d\u0941\u091c \u0915\u0947 \u0935\u093f\u0915\u0930\u094d\u0923 \u092c\u0930\u093e\u092c\u0930 \u0939\u094b\u0902, \u0924\u094b \u0926\u0930\u094d\u0936\u093e\u0907\u090f \u0915\u093f \u0935\u0939 \u090f\u0915 \u0906\u092f\u0924 \u0939\u0948 |<\/strong>
\n\"NCERT
\n\u0939\u0932 :<\/strong>
\n\u0926\u093f\u092f\u093e \u0939\u0948 :<\/strong>\u00a0ABCD \u090f\u0915 \u0938\u092e\u093e\u0902\u0924\u0930 \u091a\u0924\u0941\u0930\u094d\u092d\u0941\u091c \u0939\u0948 |
\n\u091c\u093f\u0938\u0915\u0947 \u0935\u093f\u0915\u0930\u094d\u0923 AC = BD \u0939\u0948 |
\n\u0938\u093f\u0926\u094d\u0927 \u0915\u0930\u0928\u093e \u0939\u0948 :<\/strong>\u00a0ABCD \u090f\u0915 \u0906\u092f\u0924 \u0939\u0948 |
\n\u092a\u094d\u0930\u092e\u093e\u0923 :<\/strong>\u00a0\u0394ABD \u0924\u0925\u093e \u0394ABC \u092e\u0947\u0902
\nAD = BC (\u0938\u092e\u093e\u0902\u0924\u0930 \u091a\u0924\u0941\u0930\u094d\u092d\u0941\u091c \u0915\u0940 \u0938\u092e\u094d\u092e\u0941\u0916 \u092d\u0941\u091c\u093e)
\nAB = AB (\u0909\u092d\u092f\u0928\u093f\u0937\u094d\u0920)
\nBD = AC (\u0926\u093f\u092f\u093e \u0939\u0948)
\nSSS \u0938\u0930\u094d\u0935\u093e\u0902\u0917\u0938\u092e\u0924\u093e \u0928\u093f\u092f\u092e \u0938\u0947
\n\u0394ABD\u00a0\u2245\u00a0\u0394ABC
\n\u2234\u00a0\u2220A =\u00a0\u2220B (By CPCT) \u2026\u2026 (1)
\n\u091a\u0942\u0901\u0915\u093f ABCD \u090f\u0915 \u0938\u092e\u093e\u0902\u0924\u0930 \u091a\u0924\u0941\u0930\u094d\u092d\u0941\u091c \u0939\u0948 |
\n\u2234\u00a0AD || BC \u0914\u0930 AB \u090f\u0915 \u0924\u093f\u0930\u094d\u092f\u0915 \u0930\u0947\u0916\u093e \u0939\u0948 |
\n\u0905\u0924:\u00a0\u2220A +\u00a0\u2220B = 180o<\/sup>\u00a0 (\u0905\u0902\u0924: \u0906\u0938\u0928\u094d\u0928 \u0915\u094b\u0923\u094b\u0902 \u0915\u093e \u092f\u094b\u0917)
\n\u21d2\u2220A +\u00a0\u2220A = 180o<\/sup>\u00a0 ..\u0938\u092e\u0940o (1) \u0938\u0947
\n\"NCERT
\n\u21d2 2\u2220A = 180o<\/sup>
\n\u21d2 \u2220A = 90o<\/sup>
\n(\u0935\u0939 \u0938\u092e\u093e\u0902\u0924\u0930 \u091a\u0924\u0941\u0930\u094d\u092d\u0941\u091c \u091c\u093f\u0938\u0915\u0940 \u090f\u0915 \u0915\u094b\u0923 \u0938\u092e\u0915\u094b\u0923 \u0939\u094b \u0906\u092f\u0924 \u0915\u0939\u0932\u093e\u0924\u093e \u0939\u0948)
\n\u0905\u0924: ABCD \u090f\u0915 \u0906\u092f\u0924 \u0939\u0948 | proved<\/p>\n

Ex 8.1 Class 9 \u0917\u0923\u093f\u0924\u00a0Q3. \u0926\u0930\u094d\u0936\u093e\u0907\u090f \u0915\u093f \u092f\u0926\u093f \u090f\u0915 \u091a\u0924\u0941\u0930\u094d\u092d\u0941\u091c \u0915\u0947 \u0935\u093f\u0915\u0930\u094d\u0923 \u092a\u0930\u0938\u094d\u092a\u0930 \u0938\u092e\u0915\u094b\u0923 \u092a\u0930 \u0938\u092e\u0926\u094d\u0935\u093f\u092d\u093e\u091c\u093f\u0924 \u0915\u0930\u0947\u0902, \u0924\u094b \u0935\u0939 \u090f\u0915 \u0938\u092e\u091a\u0924\u0941\u0930\u094d\u092d\u0941\u091c \u0939\u094b\u0924\u093e \u0939\u0948\u0964<\/strong>
\n\"NCERT
\n\u0939\u0932 :<\/strong>
\n\u0926\u093f\u092f\u093e \u0939\u0948 :<\/strong>\u00a0ABCD \u090f\u0915 \u091a\u0924\u0941\u0930\u094d\u092d\u0941\u091c \u0939\u0948 |
\n\u091c\u093f\u0938\u0915\u0947 \u0935\u093f\u0915\u0930\u094d\u0923 AC \u0924\u0925\u093e BD \u090f\u0915 \u0926\u0941\u0938\u0930\u0947 \u0915\u094b \u092c\u093f\u0902\u0926\u0941 O
\n\u092a\u0930 \u0938\u092e\u0926\u094d\u0935\u093f\u092d\u093e\u091c\u093f\u0924 \u0915\u0930\u0924\u0947 \u0939\u0948\u0902| \u091c\u0939\u093e\u0901\u00a0\u2220COD = 90o<\/sup>\u00a0\u0939\u0948
\n\u0914\u0930 AO = CO \u0924\u0925\u093e BO = DO \u0939\u0948|
\n\u0938\u093f\u0926\u094d\u0927 \u0915\u0930\u0928\u093e \u0939\u0948 :<\/strong>\u00a0ABCD \u090f\u0915 \u0906\u092f\u0924 \u0939\u0948 |
\n\u092a\u094d\u0930\u092e\u093e\u0923 :<\/strong>\u00a0\u0394AOB \u0924\u0925\u093e\u00a0\u0394COD \u092e\u0947\u0902
\nAO = CO (\u0926\u093f\u092f\u093e \u0939\u0948)
\nBO = DO (\u0926\u093f\u092f\u093e \u0939\u0948)
\n\u2220AOB =\u00a0\u2220COD (\u0936\u093f\u0930\u094d\u0937\u093e\u092d\u093f\u092e\u0941\u0916 \u0915\u094b\u0923)
\n\u0905\u0924: SAS \u0938\u0930\u094d\u0935\u093e\u0902\u0917\u0938\u092e\u0924\u093e \u0928\u093f\u092f\u092e \u0938\u0947
\n\u0394AOB\u00a0\u2245\u00a0\u0394COD
\n\u2234\u00a0AB = CD\u00a0(By CPCT) ………. (1)
\n\u0924\u0925\u093e\u00a0\u2220BAO =\u00a0\u2220DCO (\u090f\u0915\u093e\u0902\u0924\u0930 \u0915\u094b\u0923)\u00a0(By CPCT)
\n\u2234\u00a0AB || CD ……… (2) (\u090f\u0915\u093e\u0902\u0924\u0930 \u0915\u094b\u0923 \u092c\u0930\u093e\u092c\u0930 \u0939\u094b \u0924\u094b \u0930\u0947\u0916\u093e\u090f\u0901 \u0938\u092e\u093e\u0902\u0924\u0930 \u0939\u094b\u0924\u0940 \u0939\u0948<\/em>\u00a0)
\n\u0938\u092e\u0940o (1) \u0924\u0925\u093e (2) \u0938\u0947
\nABCD \u090f\u0915 \u0938\u092e\u093e\u0902\u0924\u0930 \u091a\u0924\u0941\u0930\u094d\u092d\u0941\u091c \u0939\u0948 |
\n(\u092f\u0926\u093f \u0915\u093f\u0938\u0940 \u091a\u0924\u0941\u0930\u094d\u092d\u0941\u091c \u0915\u0940 \u0938\u092e\u094d\u092e\u0941\u0916 \u092d\u0941\u091c\u093e\u0913\u0902 \u0915\u093e \u090f\u0915 \u092f\u0941\u0917\u094d\u092e \u092c\u0930\u093e\u092c\u0930 \u090f\u0935\u0902 \u0938\u092e\u093e\u0928\u094d\u0924\u0930 \u0939\u094b \u0924\u094b \u0935\u0939 \u0938\u092e\u093e\u0928\u094d\u0924\u0930 \u091a\u0924\u0941\u0930\u094d\u092d\u0941\u091c \u0939\u094b\u0924\u093e \u0939\u0948 |<\/em>)
\n\u2234\u00a0AD = BC ……….. (3) (\u0938\u092e\u093e\u0902\u0924\u0930 \u091a\u0924\u0941\u0930\u094d\u092d\u0941\u091c \u0915\u0940 \u0938\u092e\u094d\u092e\u0941\u0916 \u092d\u0941\u091c\u093e \u092c\u0930\u093e\u092c\u0930 \u0939\u094b\u0924\u0940 \u0939\u0948<\/em>)
\n\u0905\u092c\u00a0\u0394AOD \u0924\u0925\u093e\u00a0\u0394COD \u092e\u0947\u0902
\nAO = CO (\u0926\u093f\u092f\u093e \u0939\u0948)
\nDO = DO (\u0909\u092d\u092f\u0928\u093f\u0937\u094d\u0920)
\n\u2220AOD =\u00a0\u2220COD (90o<\/sup>\u00a0\u092a\u094d\u0930\u0924\u094d\u092f\u0947\u0915)
\n\u0905\u0924: SAS \u0938\u0930\u094d\u0935\u093e\u0902\u0917\u0938\u092e\u0924\u093e \u0928\u093f\u092f\u092e \u0938\u0947
\n\u0394AOD\u00a0\u2245\u00a0\u0394COD
\n\u2234\u00a0AD = CD\u00a0(By CPCT)\u00a0\u2026\u2026 (4)
\n\u0938\u092e\u0940o (1), (3) \u0924\u0925\u093e (4) \u0938\u0947 \u0939\u092e \u092a\u093e\u0924\u0947 \u0939\u0948\u0902 |
\nAB = BC = CD = AD
\n\u0905\u0924: ABCD \u090f\u0915 \u0938\u092e\u091a\u0924\u0941\u0930\u094d\u092d\u0941\u091c \u0939\u0948 | (Proved)
\n(\u0935\u0939 \u0938\u092e\u093e\u0928\u094d\u0924\u0930 \u091a\u0924\u0941\u0930\u094d\u092d\u0941\u091c \u091c\u093f\u0938\u0915\u0940 \u092a\u094d\u0930\u0924\u094d\u092f\u0947\u0915 \u092d\u0941\u091c\u093e \u092c\u0930\u093e\u092c\u0930 \u0939\u094b \u0938\u092e\u091a\u0924\u0941\u0930\u094d\u092d\u0941\u091c \u0939\u094b\u0924\u093e \u0939\u0948 |)<\/p>\n

Ex 8.1 Class 9 \u0917\u0923\u093f\u0924\u00a0Q4. \u0926\u0930\u094d\u0936\u093e\u0907\u090f \u0915\u093f \u090f\u0915 \u0935\u0930\u094d\u0917 \u0915\u0947 \u0935\u093f\u0915\u0930\u094d\u0923 \u092c\u0930\u093e\u092c\u0930 \u0939\u094b\u0924\u0947 \u0939\u0948\u0902 \u0914\u0930 \u092a\u0930\u0938\u094d\u092a\u0930 \u0938\u092e\u0915\u094b\u0923 \u092a\u0930 \u0938\u092e\u0926\u094d\u0935\u093f\u092d\u093e\u091c\u093f\u0924 \u0915\u0930\u0924\u0947 \u0939\u0948\u0902 |\u00a0<\/strong>
\n\"Maths
\n\u0939\u0932 :<\/strong>
\n\u0926\u093f\u092f\u093e \u0939\u0948 :<\/strong>\u00a0ABCD \u090f\u0915 \u0935\u0930\u094d\u0917 \u0939\u0948 \u091c\u093f\u0938\u0915\u0947 \u0935\u093f\u0915\u0930\u094d\u0923 AC \u0924\u0925\u093e BD \u090f\u0915
\n\u0926\u0941\u0938\u0930\u0947 \u0915\u094b \u092c\u093f\u0902\u0926\u0941 O \u092a\u0930 \u092a\u094d\u0930\u0924\u093f\u091a\u094d\u091b\u0947\u0926 \u0915\u0930\u0924\u0947 \u0939\u0948 |
\n\u0938\u093f\u0926\u094d\u0927 \u0915\u0930\u0928\u093e \u0939\u0948 :<\/strong>
\n(i) AO = CO \u0924\u0925\u093e BO = DO
\n(ii)\u00a0AOB = 90o<\/sup>
\n\u092a\u094d\u0930\u092e\u093e\u0923 :<\/strong>\u00a0\u0394AOB \u0924\u0925\u093e\u00a0\u0394COD \u092e\u0947\u0902
\nAB = CD (\u0935\u0930\u094d\u0917 \u0915\u0940 \u092d\u0941\u091c\u093e)
\n\u2220BAO =\u00a0\u2220DCO (\u090f\u0915\u093e\u0902\u0924\u0930 \u0915\u094b\u0923)
\n\u2220AOB\u00a0=\u00a0\u2220COD\u00a0(\u0936\u093f\u0930\u094d\u0937\u093e\u092d\u093f\u092e\u0941\u0916 \u0915\u094b\u0923)
\n\u0905\u0924: ASA \u0938\u0930\u094d\u0935\u093e\u0902\u0917\u0938\u092e\u0924\u093e \u0928\u093f\u092f\u092e \u0938\u0947
\n\u0394AOB\u00a0\u2245\u00a0\u0394COD
\n\u2234\u00a0AO = CO \u0924\u0925\u093e BO = DO (By CPCT) ……….. (1)
\n\u092a\u0941\u0928: \u0394AOB \u0924\u0925\u093e\u00a0\u0394BOC \u092e\u0947\u0902
\nAB = BC\u00a0(\u0935\u0930\u094d\u0917 \u0915\u0940 \u092d\u0941\u091c\u093e)
\nBO =\u00a0BO\u00a0(\u0909\u092d\u092f\u0928\u093f\u0937\u094d\u0920)
\nAO = CO\u00a0 \u0938\u092e\u0940o (1) \u0938\u0947
\n\u0905\u0924: SSS\u00a0\u0938\u0930\u094d\u0935\u093e\u0902\u0917\u0938\u092e\u0924\u093e \u0928\u093f\u092f\u092e \u0938\u0947
\n\u0394AOB\u00a0\u2245\u00a0\u0394BOC
\n\u200b\u0905\u0924:\u00a0\u2220AOB\u00a0=\u00a0\u2220COB\u00a0\u00a0(By CPCT) \u00a0 ……….. (2)
\n\u0905\u092c \u2220AOB +\u00a0\u2220COB = 180o<\/sup>\u00a0 (\u0930\u0948\u0916\u093f\u0915 \u092f\u0941\u0917\u094d\u092e)
\n\u21d2 \u2220AOB\u00a0+\u00a0\u2220AOB\u00a0= 180o<\/sup>\u00a0 \u0938\u092e\u09400 (2) \u0938\u0947
\n\u21d2 2\u2220AOB\u00a0= 180o<\/sup>
\n\u21d2 \u2220AOB\u00a0= 90o<\/sup>
\nProved.<\/p>\n

Ex 8.1 Class 9 \u0917\u0923\u093f\u0924\u00a0Q5. \u0926\u0930\u094d\u0936\u093e\u0907\u090f \u0915\u093f \u092f\u0926\u093f \u090f\u0915 \u091a\u0924\u0941\u0930\u094d\u092d\u0941\u091c \u0915\u0947 \u0935\u093f\u0915\u0930\u094d\u0923 \u092c\u0930\u093e\u092c\u0930 \u0939\u094b \u0914\u0930 \u092a\u0930\u0938\u094d\u092a\u0930 \u0938\u092e\u0926\u094d\u0935\u093f\u092d\u093e\u091c\u093f\u0924 \u0915\u0930\u0947\u0902, \u0924\u094b \u0935\u0939 \u090f\u0915 \u0935\u0930\u094d\u0917 \u0939\u094b\u0924\u093e \u0939\u0948 |<\/strong>
\n\"Class
\n\u0939\u0932 :<\/strong>
\n\u0926\u093f\u092f\u093e \u0939\u0948 :<\/strong>\u00a0ABCD \u090f\u0915\u091a\u0924\u0941\u0930\u094d\u092d\u0941\u091c \u0939\u0948 \u091c\u093f\u0938\u092e\u0947\u0902\u00a0\u0935\u093f\u0915\u0930\u094d\u0923 AC = BD \u0939\u0948 \u0914\u0930 \u090f\u0915
\n\u0926\u0941\u0938\u0930\u0947 \u0915\u094b \u092c\u093f\u0902\u0926\u0941 O \u092a\u0930 \u092a\u094d\u0930\u0924\u093f\u091a\u094d\u091b\u0947\u0926 \u0915\u0930\u0924\u0947 \u0939\u0948 | \u091c\u0939\u093e\u0901\u00a0AO = CO \u0924\u0925\u093e BO = DO \u0939\u0948 |
\n\u0938\u093f\u0926\u094d\u0927 \u0915\u0930\u0928\u093e \u0939\u0948 :\u00a0<\/strong>ABCD \u090f\u0915 \u0935\u0930\u094d\u0917 \u0939\u0948 |
\n\u092a\u094d\u0930\u092e\u093e\u0923 :<\/strong>\u00a0\u0394AOB \u0924\u0925\u093e\u00a0\u0394COD \u092e\u0947\u0902
\nAO = CO (\u0926\u093f\u092f\u093e \u0939\u0948)
\nBO = DO (\u0926\u093f\u092f\u093e \u0939\u0948)
\n\u2220AOB =\u00a0\u2220COD (\u0936\u093f\u0930\u094d\u0937\u093e\u092d\u093f\u092e\u0941\u0916 \u0915\u094b\u0923)
\n\u0905\u0924: SAS \u0938\u0930\u094d\u0935\u093e\u0902\u0917\u0938\u092e\u0924\u093e \u0928\u093f\u092f\u092e \u0938\u0947
\n\u0394AOB\u00a0\u2245\u00a0\u0394COD
\n\u2234\u00a0AB = CD(By CPCT)\u00a0\u2026\u2026 (1)
\n\u0924\u0925\u093e\u00a0\u2220BAO =\u00a0\u2220DCO (\u090f\u0915\u093e\u0902\u0924\u0930 \u0915\u094b\u0923)(By CPCT)
\n\u2234\u00a0AB || CD ……… (2) (\u090f\u0915\u093e\u0902\u0924\u0930 \u0915\u094b\u0923 \u092c\u0930\u093e\u092c\u0930 \u0939\u094b \u0924\u094b \u0930\u0947\u0916\u093e\u090f\u0901 \u0938\u092e\u093e\u0902\u0924\u0930 \u0939\u094b\u0924\u0940 \u0939\u0948\u00a0)
\n\u0938\u092e\u0940o (1) \u0924\u0925\u093e (2) \u0938\u0947
\nABCD \u090f\u0915 \u0938\u092e\u093e\u0902\u0924\u0930 \u091a\u0924\u0941\u0930\u094d\u092d\u0941\u091c \u0939\u0948 |
\n(\u092f\u0926\u093f \u0915\u093f\u0938\u0940 \u091a\u0924\u0941\u0930\u094d\u092d\u0941\u091c \u0915\u0940 \u0938\u092e\u094d\u092e\u0941\u0916 \u092d\u0941\u091c\u093e\u0913\u0902 \u0915\u093e \u090f\u0915 \u092f\u0941\u0917\u094d\u092e \u092c\u0930\u093e\u092c\u0930 \u090f\u0935\u0902 \u0938\u092e\u093e\u0928\u094d\u0924\u0930 \u0939\u094b \u0924\u094b \u0935\u0939 \u0938\u092e\u093e\u0928\u094d\u0924\u0930 \u091a\u0924\u0941\u0930\u094d\u092d\u0941\u091c \u0939\u094b\u0924\u093e \u0939\u0948 |)
\n\u2234\u00a0AD = BC ……….. (3) (\u0938\u092e\u093e\u0902\u0924\u0930 \u091a\u0924\u0941\u0930\u094d\u092d\u0941\u091c \u0915\u0940 \u0938\u092e\u094d\u092e\u0941\u0916 \u092d\u0941\u091c\u093e \u092c\u0930\u093e\u092c\u0930 \u0939\u094b\u0924\u0940 \u0939\u0948)
\n\u0905\u092c\u00a0\u0394AOD \u0924\u0925\u093e\u00a0\u0394COD \u092e\u0947\u0902
\nAO = CO (\u0926\u093f\u092f\u093e \u0939\u0948)
\nDO = DO (\u0909\u092d\u092f\u0928\u093f\u0937\u094d\u0920)
\n\u2220AOD =\u00a0\u2220COD (90o<\/sup>\u00a0\u092a\u094d\u0930\u0924\u094d\u092f\u0947\u0915)
\n\u0905\u0924: SAS \u0938\u0930\u094d\u0935\u093e\u0902\u0917\u0938\u092e\u0924\u093e \u0928\u093f\u092f\u092e \u0938\u0947
\n\u0394AOD\u00a0\u2245\u00a0\u0394COD
\n\u2234\u00a0AD = CD\u00a0(By CPCT)<\/strong>\u00a0\u2026\u2026 (4)
\n\u0938\u092e\u0940o (1), (3) \u0924\u0925\u093e (4) \u0938\u0947 \u0939\u092e \u092a\u093e\u0924\u0947 \u0939\u0948\u0902 |
\nAB = BC = CD = AD ……….. (5)
\n\u0905\u092c, \u0394ABD \u0924\u0925\u093e \u0394ABC\u00a0\u092e\u0947\u0902
\nAD = BC (\u0935\u0930\u094d\u0917 \u0915\u0940 \u0938\u092e\u094d\u092e\u0941\u0916 \u092d\u0941\u091c\u093e)
\nAB = AB (\u0909\u092d\u092f\u0928\u093f\u0937\u094d\u0920)
\nBD = AC (\u0926\u093f\u092f\u093e \u0939\u0948)
\nSSS \u0938\u0930\u094d\u0935\u093e\u0902\u0917\u0938\u092e\u0924\u093e \u0928\u093f\u092f\u092e \u0938\u0947
\n\u0394ABD\u00a0\u2245\u00a0\u0394ABD
\n\u2234\u00a0\u2220A =\u00a0\u2220B (By CPCT) \u2026\u2026 (6)
\n\u091a\u0942\u0901\u0915\u093f ABCD \u090f\u0915 \u0935\u0930\u094d\u0917 \u0939\u0948|
\n\u2234\u00a0AD || BC \u0914\u0930 AB \u090f\u0915 \u0924\u093f\u0930\u094d\u092f\u0915 \u0930\u0947\u0916\u093e \u0939\u0948 |
\n\u0905\u0924:\u00a0\u2220A +\u00a0\u2220B = 180o<\/sup>\u00a0 (\u0905\u0902\u0924: \u0906\u0938\u0928\u094d\u0928 \u0915\u094b\u0923\u094b\u0902 \u0915\u093e \u092f\u094b\u0917)
\n\u21d2 \u2220A +\u00a0\u2220A = 180o<\/sup>\u00a0 ..\u0938\u092e\u0940o (6) \u0938\u0947
\n\u21d2 2\u2220A = 180o<\/sup>
\n\"NCERT
\n\u21d2 \u2220A = 90o <\/sup>………. (7)
\n\u0938\u092e\u0940o (5) \u0924\u0925\u093e (7) \u0938\u0947 \u0938\u094d\u092a\u0937\u094d\u091f \u0939\u0948 \u0915\u093f
\nABCD \u090f\u0915 \u0935\u0930\u094d\u0917 \u0939\u0948|
\nProved.<\/p>\n

Ex 8.1 Class 9 \u0917\u0923\u093f\u0924\u00a0Q6. \u0938\u092e\u093e\u0902\u0924\u0930 \u091a\u0924\u0941\u0930\u094d\u092d\u0941\u091c ABCD \u0915\u093e \u0935\u093f\u0915\u0930\u094d\u0923 AC \u0915\u094b\u0923 A \u0915\u094b \u0938\u092e\u0926\u094d\u0935\u093f\u092d\u093e\u091c\u093f\u0924 \u0915\u0930\u0924\u093e \u0939\u0948 | \u0926\u0930\u094d\u0936\u093e\u0907\u090f \u0915\u093f<\/strong>
\n(i) \u092f\u0939\u00a0\u2220C \u0915\u094b \u092d\u0940 \u0938\u092e\u0926\u094d\u0935\u093f\u092d\u093e\u091c\u093f\u0924 \u0915\u0930\u0924\u093e \u0939\u0948 |<\/strong>
\n(ii) ABCD \u090f\u0915 \u0938\u092e\u091a\u0924\u0941\u0930\u094d\u092d\u0941\u091c \u0939\u0948 |\u00a0<\/strong>
\n\"NCERT
\n\u0939\u0932 :<\/strong>
\n\u0926\u093f\u092f\u093e \u0939\u0948 :\u00a0<\/strong>ABCD \u090f\u0915\u00a0\u0938\u092e\u093e\u0902\u0924\u0930 \u091a\u0924\u0941\u0930\u094d\u092d\u0941\u091c\u00a0\u0939\u0948 \u091c\u093f\u0938\u0915\u093e
\n\u0935\u093f\u0915\u0930\u094d\u0923 AC \u0915\u094b\u0923 A \u0915\u094b\u00a0\u0938\u092e\u0926\u094d\u0935\u093f\u092d\u093e\u091c\u093f\u0924 \u0915\u0930\u0924\u093e \u0939\u0948 |
\n\u0938\u093f\u0926\u094d\u0927 \u0915\u0930\u0928\u093e \u0939\u0948 :\u00a0<\/strong>
\n(i) AC, \u2220C \u0915\u094b \u092d\u0940 \u0938\u092e\u0926\u094d\u0935\u093f\u092d\u093e\u091c\u093f\u0924 \u0915\u0930\u0924\u093e \u0939\u0948 |
\n(ii) ABCD \u090f\u0915 \u0938\u092e\u091a\u0924\u0941\u0930\u094d\u092d\u0941\u091c \u0939\u0948 |
\n\u092a\u094d\u0930\u092e\u093e\u0923:<\/strong>
\n(i) \u0394ABC \u0924\u0925\u093e\u00a0\u0394DAC \u092e\u0947\u0902,
\n\u2220BAC\u00a0=\u00a0\u2220BAC\u00a0\u00a0(\u0926\u093f\u092f\u093e \u0939\u0948)
\n\u2220B\u00a0=\u00a0\u2220D\u00a0(\u0938\u092e\u093e\u0902\u0924\u0930 \u091a\u0924\u0941\u0930\u094d\u092d\u0941\u091c \u0915\u0947 \u0938\u092e\u094d\u092e\u0941\u0916 \u0915\u094b\u0923 \u092c\u0930\u093e\u092c\u0930 \u0939\u094b\u0924\u0947 \u0939\u0948 )
\nAC = AC (\u0909\u092d\u092f\u0928\u093f\u0937\u094d\u0920)
\n\u0905\u0924: ASA \u0938\u0930\u094d\u0935\u093e\u0902\u0917\u0938\u092e\u0924\u093e \u0928\u093f\u092f\u092e \u0938\u0947
\n\u0394ABC \u2245\u00a0\u0394DAC
\n\u2234\u00a0\u2220BCA\u00a0=\u00a0\u2220DCA (By CPCT<\/strong>)
\n\u0905\u0924: \u0935\u093f\u0915\u0930\u094d\u0923 AC,\u00a0\u2220C \u0915\u094b \u0938\u092e\u0926\u094d\u0935\u093f\u092d\u093e\u091c\u093f\u0924 \u0915\u0930\u0924\u093e \u0939\u0948 |<\/p>\n

\u200b(ii) \u092a\u0941\u0928: AB = AD \u00a0 \u00a0(By\u00a0CPCT)\u00a0 ……………. (1)
\n\u091a\u0942\u0901\u0915\u093f ABCD\u00a0\u090f\u0915\u00a0\u0938\u092e\u093e\u0902\u0924\u0930 \u091a\u0924\u0941\u0930\u094d\u092d\u0941\u091c\u00a0\u0939\u0948 |
\n\u2234 AB = CD \u00a0 (\u0938\u092e\u093e\u0902\u0924\u0930 \u091a\u0924\u0941\u0930\u094d\u092d\u0941\u091c \u0915\u0940 \u0938\u092e\u094d\u092e\u0941\u0916 \u092d\u0941\u091c\u093e )\u00a0……(2)
\n\u0914\u0930
\nBC = AD \u00a0 (\u0938\u092e\u093e\u0902\u0924\u0930 \u091a\u0924\u0941\u0930\u094d\u092d\u0941\u091c \u0915\u0940 \u0938\u092e\u094d\u092e\u0941\u0916 \u092d\u0941\u091c\u093e )\u00a0……(3)
\n\u0938\u092e\u0940\u0915\u0930\u0923 (1), (2) \u0924\u0925\u093e (3) \u0938\u0947
\nAB = BC = CD = AD
\n\u0905\u0924: ABCD \u090f\u0915\u00a0\u0938\u092e\u091a\u0924\u0941\u0930\u094d\u092d\u0941\u091c \u0939\u0948 |\u00a0(Proved)<\/p>\n

Ex 8.1 Class 9 \u0917\u0923\u093f\u0924\u00a0Q7. ABCD \u090f\u0915\u00a0\u0938\u092e\u091a\u0924\u0941\u0930\u094d\u092d\u0941\u091c \u0939\u0948 | \u0926\u0930\u094d\u0936\u093e\u0907\u090f \u0915\u093f AC \u0915\u094b\u0923\u094b\u0902 A \u0914\u0930 C \u0926\u094b\u0928\u094b\u0902 \u0915\u094b \u0938\u092e\u0926\u094d\u0935\u093f\u092d\u093e\u091c\u093f\u0924 \u0915\u0930\u0924\u093e \u0939\u0948 \u0924\u0925\u093e \u0935\u093f\u0915\u0930\u094d\u0923 BD \u0915\u094b\u0923\u094b\u0902 B \u0924\u0925\u093e D \u0926\u094b\u0928\u094b\u0902 \u0915\u094b \u0938\u092e\u0926\u094d\u0935\u093f\u092d\u093e\u091c\u093f\u0924 \u0915\u0930\u0924\u093e \u0939\u0948|\u00a0<\/strong>
\n\"NCERT
\n\u0939\u0932 :<\/strong>
\n\u0926\u093f\u092f\u093e \u0939\u0948 :\u00a0<\/strong>ABCD \u090f\u0915\u00a0\u0938\u092e\u091a\u0924\u0941\u0930\u094d\u092d\u0941\u091c\u00a0\u091a\u0924\u0941\u0930\u094d\u092d\u0941\u091c\u00a0\u0939\u0948 |
\n\u0938\u093f\u0926\u094d\u0927 \u0915\u0930\u0928\u093e \u0939\u0948 :\u00a0<\/strong>
\n(i) AC,\u00a0\u2220A\u00a0\u0924\u0925\u093e\u00a0\u2220C \u0915\u094b \u092d\u0940 \u0938\u092e\u0926\u094d\u0935\u093f\u092d\u093e\u091c\u093f\u0924 \u0915\u0930\u0924\u093e \u0939\u0948 |
\n(ii) BD,\u00a0\u2220B\u00a0\u0924\u0925\u093e\u00a0\u2220D \u0915\u094b \u092d\u0940 \u0938\u092e\u0926\u094d\u0935\u093f\u092d\u093e\u091c\u093f\u0924 \u0915\u0930\u0924\u093e \u0939\u0948 |
\n\u092a\u094d\u0930\u092e\u093e\u0923:<\/strong>
\n(i) \u0394ABC \u0924\u0925\u093e\u00a0\u0394ADC \u092e\u0947\u0902,
\nAB\u00a0= AD \u00a0(\u0938\u092e\u091a\u0924\u0941\u0930\u094d\u092d\u0941\u091c \u0915\u0940 \u092d\u0941\u091c\u093e\u090f\u0901)
\n\u2220B\u00a0=\u00a0\u2220D \u00a0(\u0938\u092e\u091a\u0924\u0941\u0930\u094d\u092d\u0941\u091c\u00a0\u0915\u0947 \u0938\u092e\u094d\u092e\u0941\u0916 \u0915\u094b\u0923 \u092c\u0930\u093e\u092c\u0930 \u0939\u094b\u0924\u0947 \u0939\u0948 )
\nAC = AC (\u0909\u092d\u092f\u0928\u093f\u0937\u094d\u0920)
\n\u0905\u0924: SAS \u0938\u0930\u094d\u0935\u093e\u0902\u0917\u0938\u092e\u0924\u093e \u0928\u093f\u092f\u092e \u0938\u0947
\n\u0394ABC \u2245\u00a0\u0394ADC
\n\u2234\u00a0\u2220BAC =\u00a0\u2220DAC (By CPCT<\/strong>) ……………. (1)
\n\u2234\u00a0\u2220BCA\u00a0=\u00a0\u2220DCA (By CPCT<\/strong>) …………….(2)
\n\u0938\u092e\u0940o (1) \u0924\u0925\u093e (2) \u0938\u0947
\n\u0935\u093f\u0915\u0930\u094d\u0923 AC,\u00a0\u2220A \u0924\u0925\u093e\u00a0\u2220C \u0915\u094b \u0938\u092e\u0926\u094d\u0935\u093f\u092d\u093e\u091c\u093f\u0924 \u0915\u0930\u0924\u093e \u0939\u0948 |
\n\u0907\u0938\u0940 \u092a\u094d\u0930\u0915\u093e\u0930 \u0939\u092e<\/p>\n

(ii) BD,\u00a0\u2220B\u00a0\u0924\u0925\u093e\u00a0\u2220D \u0915\u094b \u092d\u0940 \u0938\u092e\u0926\u094d\u0935\u093f\u092d\u093e\u091c\u093f\u0924 \u0915\u0930\u0924\u093e \u0939\u0948 |
\n\u0915\u094b \u092d\u0940 \u0938\u093f\u0926\u094d\u0927 \u0915\u0930 \u0938\u0915\u0924\u0947 \u0939\u0948\u0902|<\/p>\n

Ex 8.1 Class 9 \u0917\u0923\u093f\u0924\u00a0Q8. ABCD\u00a0<\/strong>\u090f\u0915 \u0906\u092f\u0924 \u0939\u0948 \u091c\u093f\u0938\u092e\u0947\u0902 \u0935\u093f\u0915\u0930\u094d\u0923 AC \u0926\u094b\u0928\u094b\u0902 \u0915\u094b\u0923 A \u0914\u0930 C \u0915\u094b \u0938\u092e\u0926\u094d\u0935\u093f\u092d\u093e\u091c\u093f\u0924 \u0915\u0930\u0924\u093e \u0939\u0948 | \u0926\u0930\u094d\u0936\u093e\u0907\u090f \u0915\u093f:<\/strong>
\n(i) ABCD \u090f\u0915 \u0935\u0930\u094d\u0917 \u0939\u0948 |<\/strong>
\n(ii) \u0935\u093f\u0915\u0930\u094d\u0923 BD \u0926\u094b\u0928\u094b\u0902 \u0915\u094b\u0923 B \u0914\u0930 D \u0915\u094b \u0938\u092e\u0926\u094d\u0935\u093f\u092d\u093e\u091c\u093f\u0924 \u0915\u0930\u0924\u093e \u0939\u0948<\/strong>
\n\"NCERT
\n\u0939\u0932 :<\/strong>
\n\u0926\u093f\u092f\u093e \u0939\u0948:<\/strong>\u00a0ABCD \u090f\u0915 \u0906\u092f\u0924 \u0939\u0948 \u091c\u093f\u0938\u092e\u0947\u0902 \u0935\u093f\u0915\u0930\u094d\u0923 AC \u0926\u094b\u0928\u094b\u0902 \u0915\u094b\u0923 A \u0914\u0930 C \u0915\u094b \u0938\u092e\u0926\u094d\u0935\u093f\u092d\u093e\u091c\u093f\u0924 \u0915\u0930\u0924\u093e \u0939\u0948 |
\n\u0938\u093f\u0926\u094d\u0927 \u0915\u0930\u0928\u093e \u0939\u0948 :<\/strong>
\n(i) ABCD \u090f\u0915 \u0935\u0930\u094d\u0917 \u0939\u0948|
\n(ii) \u0935\u093f\u0915\u0930\u094d\u0923 BD \u0926\u094b\u0928\u094b\u0902 \u0915\u094b\u0923 B \u0914\u0930 D \u0915\u094b \u0938\u092e\u0926\u094d\u0935\u093f\u092d\u093e\u091c\u093f\u0924 \u0915\u0930\u0924\u093e \u0939\u0948 |
\n\u092a\u094d\u0930\u092e\u093e\u0923:<\/strong>
\n(i) \u091a\u0942\u0901\u0915\u093f ABCD \u090f\u0915 \u0906\u092f\u0924 \u0939\u0948 |
\n\u2234 AB = CD ……………… (1) \u0906\u092f\u0924 \u0915\u0940 \u0938\u092e\u094d\u092e\u0941\u0916 \u092d\u0941\u091c\u093e
\n\u0914\u0930 AD = BC ……………… (2) \u0906\u092f\u0924 \u0915\u0940 \u0938\u092e\u094d\u092e\u0941\u0916 \u092d\u0941\u091c\u093e
\n\u0905\u092c,\u00a0\u0394ABC \u0924\u0925\u093e\u00a0\u0394ACD \u092e\u0947\u0902,
\n\u2220BAC =\u00a0\u2220DAC (\u0926\u093f\u092f\u093e \u0939\u0948 ) \u091a\u0942\u0901\u0915\u093f AC \u0915\u094b\u0923 A \u0914\u0930 C \u0915\u094b \u0938\u092e\u0926\u094d\u0935\u093f\u092d\u093e\u091c\u093f\u0924 \u0915\u0930\u0924\u093e \u0939\u0948 |
\nAC = AC (\u0909\u092d\u092f\u0928\u093f\u0937\u094d\u0920)
\n\u2220B =\u00a0\u2220D (\u092a\u094d\u0930\u0924\u094d\u092f\u0947\u0915 90o<\/sup>\u00a0) \u0906\u092f\u0924 \u0915\u0947 \u0915\u094b\u0923
\nA.A.S \u0938\u0930\u094d\u0935\u093e\u0902\u0917\u0938\u092e\u0924\u093e \u0928\u093f\u092f\u092e \u0938\u0947
\n\u0394ABC\u00a0\u2245\u00a0\u0394ACD
\n\u2234\u00a0AB = AD ………….. (3) (By CPCT \/\u0938\u0930\u094d\u0935\u093e\u0902\u0917\u0938\u092e \u0924\u094d\u0930\u093f\u092d\u0941\u091c \u0915\u0947 \u0938\u0902\u0917\u0924 \u092d\u093e\u0917)
\n\u0938\u092e\u0940\u0915\u0930\u0923 (1), (2) \u0914\u0930 (3) \u0938\u0947
\nAB \u00a0= BC = CD = AD
\n\u091a\u0942\u0901\u0915\u093f ABCD \u090f\u0915 \u0906\u092f\u0924 \u0939\u0948 \u0914\u0930 \u0907\u0938\u0915\u0940 \u092a\u094d\u0930\u0924\u094d\u092f\u0947\u0915 \u092d\u0941\u091c\u093e \u092c\u0930\u093e\u092c\u0930 \u092d\u0940 \u0939\u0948 |
\n\u0905\u0924: ABCD \u090f\u0915 \u0935\u0930\u094d\u0917 \u0939\u0948|
\nProved.<\/p>\n

(ii)\u00a0\u0394ABD \u0924\u0925\u093e\u00a0\u0394CBD \u092e\u0947\u0902,
\nAB = BC (\u0935\u0930\u094d\u0917 \u0915\u0940 \u092d\u0941\u091c\u093e)
\nBD = BD (\u0909\u092d\u092f\u0928\u093f\u0937\u094d\u0920)
\n\u2220A =\u00a0\u2220C (\u092a\u094d\u0930\u0924\u094d\u092f\u0947\u0915 90o<\/sup>\u00a0) \u0935\u0930\u094d\u0917 \u0915\u0947 \u0915\u094b\u0923
\nS.A.S \u0938\u0930\u094d\u0935\u093e\u0902\u0917\u0938\u092e\u0924\u093e \u0928\u093f\u092f\u092e \u0938\u0947
\n\u0394ABD\u00a0\u2245\u00a0\u0394CBD
\n\"Maths<\/p>\n

Ex 8.1 Class 9 \u0917\u0923\u093f\u0924\u00a0Q9.\u00a0<\/strong>\u0938\u092e\u093e\u0902\u0924\u0930 \u091a\u0924\u0941\u0930\u094d\u092d\u0941\u091c\u00a0<\/strong>ABCD \u0915\u0947<\/strong>\u00a0\u0935\u093f\u0915\u0930\u094d\u0923<\/strong>\u00a0BD<\/strong>\u00a0\u092a\u0930<\/strong>\u00a0\u0926\u094b<\/strong>\u00a0\u092c\u093f\u0902\u0926\u0941<\/strong>\u00a0P<\/strong>\u00a0\u0914\u0930 Q \u0907\u0938 \u092a\u094d\u0930\u0915\u093e\u0930 \u0938\u094d\u0925\u093f\u0924 \u0939\u0948\u0902 \u0915\u093f DP = BQ \u0939\u0948\u0964 \u0926\u0930\u094d\u0936\u093e\u0907\u090f \u0915\u093f<\/strong>
\n(i) \u0394 APD\u00a0\u2245\u00a0\u0394 CQB<\/strong>
\n(ii) AP = CQ<\/strong>
\n(iii) \u0394 AQB\u00a0<\/strong>\u2245<\/strong>\u00a0\u0394 CPD<\/strong>
\n(iv) AQ = CP<\/strong>
\n(v) APCQ \u090f\u0915 \u0938\u092e\u093e\u0928\u094d\u0924\u0930 \u091a\u0924\u0941\u0930\u094d\u092d\u0941\u091c \u0939\u0948 |<\/strong>
\n\"NCERT
\n\u0939\u0932 :<\/strong>
\n\u0926\u093f\u092f\u093e \u0939\u0948 :<\/strong>\u00a0ABCD \u090f\u0915 \u0938\u092e\u093e\u0902\u0924\u0930 \u091a\u0924\u0941\u0930\u094d\u092d\u0941\u091c \u0939\u0948 \u0914\u0930 DP = BQ \u0939\u0948 |
\n\u0938\u093f\u0926\u094d\u0927 \u0915\u0930\u0928\u093e \u0939\u0948 :<\/strong>
\n(i) \u0394 APD\u00a0\u2245\u00a0\u0394 CQB
\n(ii) AP = CQ
\n(iii) \u0394 AQB\u00a0\u2245\u00a0\u0394 CPD
\n(iv) AQ = CP
\n(v) APCQ \u090f\u0915 \u0938\u092e\u093e\u0928\u094d\u0924\u0930 \u091a\u0924\u0941\u0930\u094d\u092d\u0941\u091c \u0939\u0948 |
\n\"Maths
\n\u092a\u094d\u0930\u0923\u093e\u092e :<\/strong>
\n(i) \u0394 APD \u0924\u0925\u093e \u00a0\u0394 CQB \u092e\u0947\u0902
\nAD = BC\u00a0 (\u0938\u092e\u093e\u0902\u0924\u0930 \u091a\u0924\u0941\u0930\u094d\u092d\u0941\u091c \u0915\u0940 \u0938\u092e\u094d\u092e\u0941\u0916 \u092d\u0941\u091c\u093e)
\nDP = BQ \u00a0(\u0926\u093f\u092f\u093e \u0939\u0948 )
\n\u2220ADP =\u00a0\u2220CBQ\u00a0 (\u090f\u0915\u093e\u0902\u0924\u0930 \u0905\u0924: \u0915\u094b\u0923)
\n\u0905\u0924:\u00a0 S.A.S \u0938\u0930\u094d\u0935\u093e\u0902\u0917\u0938\u092e\u0924\u093e \u0928\u093f\u092f\u092e \u0938\u0947
\n\u2234\u00a0\u00a0\u00a0 \u0394 APD\u00a0\u2245\u00a0\u0394 CQB<\/p>\n

(ii) \u0905\u0924: AP = CQ ………………. (1) (By CPCT \/\u0938\u0930\u094d\u0935\u093e\u0902\u0917\u0938\u092e \u0924\u094d\u0930\u093f\u092d\u0941\u091c \u0915\u0947 \u0938\u0902\u0917\u0924 \u092d\u093e\u0917)<\/p>\n

(iii) \u0394 AQB \u0924\u0925\u093e \u0394 CPD \u092e\u0947\u0902
\nAB = DC\u00a0 (\u0938\u092e\u093e\u0902\u0924\u0930 \u091a\u0924\u0941\u0930\u094d\u092d\u0941\u091c \u0915\u0940 \u0938\u092e\u094d\u092e\u0941\u0916 \u092d\u0941\u091c\u093e)
\nBQ = DP \u00a0(\u0926\u093f\u092f\u093e \u0939\u0948 )
\n\u2220ABQ =\u00a0\u2220CDP\u00a0 (\u090f\u0915\u093e\u0902\u0924\u0930 \u0905\u0924: \u0915\u094b\u0923)
\n\u0905\u0924:\u00a0 S.A.S \u0938\u0930\u094d\u0935\u093e\u0902\u0917\u0938\u092e\u0924\u093e \u0928\u093f\u092f\u092e \u0938\u0947
\n\u2234\u00a0\u00a0\u00a0 \u0394 AQB\u00a0\u2245\u00a0\u0394 CPD<\/p>\n

(iv) \u0905\u0924: AQ = CP ………………. (2) (By CPCT \/\u0938\u0930\u094d\u0935\u093e\u0902\u0917\u0938\u092e \u0924\u094d\u0930\u093f\u092d\u0941\u091c \u0915\u0947 \u0938\u0902\u0917\u0924 \u092d\u093e\u0917)<\/p>\n

(v) \u0938\u092e\u0940o (1) \u0924\u0925\u093e (2) \u0938\u0947
\nAPCQ \u090f\u0915 \u0938\u092e\u093e\u0928\u094d\u0924\u0930 \u091a\u0924\u0941\u0930\u094d\u092d\u0941\u091c \u0939\u0948 |<\/p>\n

Ex 8.1 Class 9 \u0917\u0923\u093f\u0924\u00a0Q10.\u00a0<\/strong>ABCD \u090f\u0915 \u0938\u092e\u093e\u0902\u0924\u0930 \u091a\u0924\u0941\u0930\u094d\u092d\u091c \u0939\u0948 \u0924\u0925\u093e AP \u0914\u0930 CQ<\/strong>
\n\u00a0\u0936\u0940\u0930\u094d\u0937\u094b\u0902 A \u0914\u0930 C \u0938\u0947 \u0935\u093f\u0915\u0930\u094d\u0923 BD \u092a\u0930 \u0915\u094d\u0930\u092e\u0936\u0903 \u0932\u092e\u094d\u092c \u0939\u0948\u0902\u0964<\/strong>
\n\u0926\u0930\u094d\u0936\u093e\u0907\u090f \u0915\u093f<\/strong>
\n(i) \u0394 APB\u00a0\u2245\u00a0\u0394 CQD<\/strong>
\n(ii) AP = CQ<\/strong>
\n\u0939\u0932 :<\/strong>
\n\"Maths
\n\u0926\u093f\u092f\u093e \u0939\u0948 :\u00a0<\/strong>ABCD \u090f\u0915 \u0938\u092e\u093e\u0902\u0924\u0930 \u091a\u0924\u0941\u0930\u094d\u092d\u091c \u0939\u0948 \u0924\u0925\u093e AP \u0914\u0930 CQ
\n\u0936\u0940\u0930\u094d\u0937\u094b\u0902 A \u0914\u0930 C \u0938\u0947 \u0935\u093f\u0915\u0930\u094d\u0923 BD \u092a\u0930 \u0915\u094d\u0930\u092e\u0936\u0903 \u0932\u092e\u094d\u092c \u0939\u0948\u0902\u0964
\n\u0938\u093f\u0926\u094d\u0927 \u0915\u0930\u0928\u093e \u0939\u0948 :<\/strong>
\n(i) \u0394 APB\u00a0\u2245\u00a0\u0394 CQD
\n(ii) AP = CQ
\n\u092a\u094d\u0930\u092e\u093e\u0923:<\/strong>
\n(i) \u0394 APB \u0924\u0925\u093e \u00a0\u0394 CQD \u092e\u0947\u0902,
\nAB = CD (\u0938\u092e\u093e\u0902\u0924\u0930 \u091a\u0924\u0941\u0930\u094d\u092d\u0941\u091c \u0915\u0940 \u0938\u092e\u094d\u092e\u0941\u0916 \u092d\u0941\u091c\u093e)
\n\u2220ABP =\u00a0\u2220CDQ\u00a0 (\u090f\u0915\u093e\u0902\u0924\u0930 \u0905\u0924: \u0915\u094b\u0923)
\n\u2220APB =\u00a0\u2220CQD \u00a0(\u092a\u094d\u0930\u0924\u094d\u092f\u0947\u0915 90o<\/sup>)
\n\u0905\u0924:, ASA \u0938\u0930\u094d\u0935\u093e\u0902\u0917\u0938\u092e\u0924\u093e \u0928\u093f\u092f\u092e \u0938\u0947
\n\u0394 APB\u00a0\u2245\u00a0\u0394 CQD
\n(ii) \u0907\u0938\u0932\u093f\u090f, AP = CQ (By CPCT \/\u0938\u0930\u094d\u0935\u093e\u0902\u0917\u0938\u092e \u0924\u094d\u0930\u093f\u092d\u0941\u091c \u0915\u0947 \u0938\u0902\u0917\u0924 \u092d\u093e\u0917)<\/p>\n

Ex 8.1 Class 9 \u0917\u0923\u093f\u0924\u00a0Q11.\u00a0<\/strong>\u0394ABC\u00a0<\/strong>\u0914\u0930\u00a0<\/strong>\u0394DEF\u00a0<\/strong>\u092e\u0947\u0902,\u00a0<\/strong>AB = DE, AB||DF, BC = EF\u00a0<\/strong>\u0914\u0930\u00a0<\/strong>BC||EF\u00a0<\/strong>\u0939\u0948 | \u0936\u0940\u0930\u094d\u0937\u094b\u0902 A, B \u0914\u0930 C \u0915\u094b \u0915\u094d\u0930\u092e\u0936: \u0936\u0940\u0930\u094d\u0937\u094b\u0902 D, E \u0914\u0930 F \u0938\u0947 \u091c\u094b\u095c\u093e \u091c\u093e\u0924\u093e \u0939\u0948| \u0926\u0930\u094d\u0936\u093e\u0907\u090f \u0915\u093f<\/strong>
\n(i)\u00a0<\/strong>\u091a\u0924\u0941\u0930\u094d\u092d\u0941\u091c<\/strong>\u00a0\u00a0ABED\u00a0<\/strong>\u090f\u0915 \u0938\u092e\u093e\u0902\u0924\u0930 \u091a\u0924\u0941\u0930\u094d\u092d\u0941\u091c \u0939\u0948\u0964<\/strong>
\n(ii)\u00a0<\/strong>\u091a\u0924\u0941\u0930\u094d\u092d\u0941\u091c<\/strong>\u00a0\u00a0BEFC\u00a0<\/strong>\u090f\u0915 \u0938\u092e\u093e\u0902\u0924\u0930 \u091a\u0924\u0941\u0930\u094d\u092d\u0941\u091c \u0939\u0948\u0964<\/strong>
\n(iii) AD || CF\u00a0<\/strong>\u0914\u0930<\/strong>\u00a0AD = CF\u00a0<\/strong>\u0939\u0948|<\/strong>
\n(iv<\/strong>\u00a0\u091a\u0924\u0941\u0930\u094d\u092d\u0941\u091c<\/strong>\u00a0\u00a0ACFD\u00a0<\/strong>\u090f\u0915 \u0938\u092e\u093e\u0902\u0924\u0930 \u091a\u0924\u0941\u0930\u094d\u092d\u0941\u091c \u0939\u0948\u0964<\/strong>
\n(v) AC = DF\u00a0<\/strong>\u0939\u0948 |<\/strong>
\n(vi) \u0394 ABC\u00a0<\/strong>\u2245\u00a0\u0394 DEF\u00a0<\/strong>\u0939\u0948 |<\/strong>
\n\u0939\u0932 :<\/strong>
\n\"Quadrilaterals
\n\u0926\u093f\u092f\u093e \u0939\u0948 :<\/strong>\u00a0\u0394ABC \u0914\u0930 \u0394DEF \u092e\u0947\u0902, AB = DE, AB||DF, BC = EF \u0914\u0930 BC||EF \u0939\u0948 |
\n\u0938\u093f\u0926\u094d\u0927 \u0915\u0930\u0928\u093e \u0939\u0948 :<\/strong>
\n(i) \u091a\u0924\u0941\u0930\u094d\u092d\u0941\u091c \u00a0ABED \u090f\u0915 \u0938\u092e\u093e\u0902\u0924\u0930 \u091a\u0924\u0941\u0930\u094d\u092d\u0941\u091c \u0939\u0948\u0964
\n(ii) \u091a\u0924\u0941\u0930\u094d\u092d\u0941\u091c \u00a0BEFC \u090f\u0915 \u0938\u092e\u093e\u0902\u0924\u0930 \u091a\u0924\u0941\u0930\u094d\u092d\u0941\u091c \u0939\u0948\u0964
\n(iii) AD || CF \u0914\u0930 AD = CF \u0939\u0948|
\n(iv \u091a\u0924\u0941\u0930\u094d\u092d\u0941\u091c \u00a0ACFD \u090f\u0915 \u0938\u092e\u093e\u0902\u0924\u0930 \u091a\u0924\u0941\u0930\u094d\u092d\u0941\u091c \u0939\u0948\u0964
\n(v) AC = DF \u0939\u0948|
\n(vi) \u0394 ABC\u00a0\u2245\u00a0\u0394 DEF \u0939\u0948 |
\n\u092a\u094d\u0930\u092e\u093e\u0923:<\/strong>
\n\"Quadrilaterals
\n(i) \u091a\u0924\u0941\u0930\u094d\u092d\u0941\u091c \u00a0ABED \u092e\u0947\u0902
\nAB = DE \u0914\u0930 AB||DF \u0926\u093f\u092f\u093e\u00a0 \u0939\u0948 |
\n\u2234\u00a0\u091a\u0924\u0941\u0930\u094d\u092d\u0941\u091c \u00a0ABED \u090f\u0915 \u0938\u092e\u093e\u0902\u0924\u0930 \u091a\u0924\u0941\u0930\u094d\u092d\u0941\u091c \u0939\u0948 |
\n( \u092f\u0926\u093f \u0915\u093f\u0938\u0940 \u091a\u0924\u0941\u0930\u094d\u092d\u0941\u091c \u0915\u0940 \u0938\u092e\u094d\u092e\u0941\u0916 \u092d\u0941\u091c\u093e\u0913\u0902 \u0915\u093e \u090f\u0915 \u092f\u0941\u0917\u094d\u092e \u092c\u0930\u093e\u092c\u0930 \u0914\u0930 \u0938\u092e\u093e\u0902\u0924\u0930 \u0939\u094b \u0924\u094b \u0935\u0939 \u0938\u092e\u093e\u0902\u0924\u0930 \u091a\u0924\u0941\u0930\u094d\u092d\u0941\u091c \u0939\u094b\u0924\u093e \u0939\u0948 )
\n\u0905\u092c, \u091a\u0942\u0901\u0915\u093f ABED \u090f\u0915 \u0938\u092e\u093e\u0902\u0924\u0930 \u091a\u0924\u0941\u0930\u094d\u092d\u0941\u091c \u0939\u0948 |
\n\u2234\u00a0AD = BE \u0914\u0930 AD|| BE ………(1)
\n(\u0938\u092e\u093e\u0902\u0924\u0930 \u091a\u0924\u0941\u0930\u094d\u092d\u0941\u091c \u0915\u0940 \u0938\u092e\u094d\u092e\u0941\u0916 \u092d\u0941\u091c\u093e \u092c\u0930\u093e\u092c\u0930 \u0914\u0930 \u0938\u092e\u093e\u0902\u0924\u0930 \u0939\u094b\u0924\u0940 \u0939\u0948)<\/p>\n

(ii) \u0907\u0938\u0940\u092a\u094d\u0930\u0915\u093e\u0930 \u0938\u0947, \u091a\u0924\u0941\u0930\u094d\u092d\u0941\u091c \u00a0BEFC \u092e\u0947\u0902
\nBC = EF \u0914\u0930 BC||EF \u0926\u093f\u092f\u093e \u0939\u0948 |
\n\u2234\u091a\u0924\u0941\u0930\u094d\u092d\u0941\u091c \u00a0BEFC \u090f\u0915 \u0938\u092e\u093e\u0902\u0924\u0930 \u091a\u0924\u0941\u0930\u094d\u092d\u0941\u091c \u0939\u0948 |
\n\u0905\u0924: CF = BE \u0914\u0930 CF||BE ……….. (2) (\u0938\u092e\u093e\u0902\u0924\u0930 \u091a\u0924\u0941\u0930\u094d\u092d\u0941\u091c \u0915\u0940 \u0938\u092e\u094d\u092e\u0941\u0916)<\/p>\n

(iii) \u0938\u092e\u0940o (1) \u0924\u0925\u093e (2) \u0938\u0947
\nAD || CF \u0914\u0930 AD = CF \u0939\u0948|
\n(\u091a\u0942\u0901\u0915\u093f \u0938\u092e\u094d\u092e\u0941\u0916 \u092d\u0941\u091c\u093e\u0913\u0902 \u0915\u093e \u090f\u0915 \u092f\u0941\u0917\u094d\u092e \u092c\u0930\u093e\u092c\u0930 \u0914\u0930 \u0938\u092e\u093e\u0902\u0924\u0930 \u0939\u0948)
\n\u2234\u091a\u0924\u0941\u0930\u094d\u092d\u0941\u091c \u00a0ACFD \u090f\u0915 \u0938\u092e\u093e\u0902\u0924\u0930 \u091a\u0924\u0941\u0930\u094d\u092d\u0941\u091c \u0939\u0948\u0964
\n\u0907\u0938\u0932\u093f\u090f, AC = DF \u0914\u0930 AC||DF ………. (3)<\/p>\n

(vi) \u0394 ABC \u0914\u0930 \u0394 DEF \u092e\u0947\u0902,
\nAB = DE (\u0926\u093f\u092f\u093e \u0939\u0948)
\nBC = EF (\u0926\u093f\u092f\u093e \u0939\u0948)
\nAC = DF (\u0938\u092e\u0940o 3 \u0938\u0947)
\nS.S.S \u0938\u0930\u094d\u0935\u093e\u0902\u0917\u0938\u092e\u0924\u093e \u0928\u093f\u092f\u092e \u0938\u0947
\n\u0394 ABC\u00a0\u2245\u00a0\u0394 DEF
\nProved.<\/p>\n

Ex 8.1 Class 9 \u0917\u0923\u093f\u0924\u00a0Q12. ABCD \u090f\u0915 \u0938\u092e\u0932\u092e\u094d\u092c \u0939\u0948, \u091c\u093f\u0938\u092e\u0947\u0902 AB || DC \u0914\u0930 AD = BC \u0939\u0948 | \u0926\u0930\u094d\u0936\u093e\u0907\u090f \u0915\u093f<\/strong>
\n(i) \u2220 A = \u2220 B<\/strong>
\n(ii) \u2220 C = \u2220 D<\/strong>
\n(iii) \u0394 ABC\u00a0\u2245\u00a0\u0394 BAD<\/strong>
\n(iv) \u0935\u093f\u0915\u0930\u094d\u0923 AC = \u0935\u093f\u0915\u0930\u094d\u0923 BD \u0939\u0948 |<\/strong>
\n\"Class
\n\u0939\u0932 :<\/strong>
\n\u0926\u093f\u092f\u093e \u0939\u0948 :<\/strong>\u00a0ABCD \u090f\u0915 \u0938\u092e\u0932\u092e\u094d\u092c \u0939\u0948,
\n\u091c\u093f\u0938\u092e\u0947\u0902 AB || DC \u0914\u0930 AD = BC \u0939\u0948 |
\n\u0938\u093f\u0926\u094d\u0927 \u0915\u0930\u0928\u093e \u0939\u0948 :<\/strong>
\n\"NCERT
\n(i) \u2220 A = \u2220 B
\n(ii) \u2220 C = \u2220 D
\n(iii) \u0394 ABC\u00a0\u2245\u00a0\u0394 BAD
\n(iv) \u0935\u093f\u0915\u0930\u094d\u0923 AC = \u0935\u093f\u0915\u0930\u094d\u0923 BD \u0939\u0948 |
\n\u0930\u091a\u0928\u093e :<\/strong>\u00a0AD \u0915\u0947 \u0938\u092e\u093e\u0902\u0924\u0930 CE \u0916\u093f\u0902\u091a\u093e |
\n\u092a\u094d\u0930\u092e\u093e\u0923:\u00a0<\/strong>AB || DC ……….. (1) \u0926\u093f\u092f\u093e \u0939\u0948 |
\nAD || CE ………… (2) \u0930\u091a\u0928\u093e \u0938\u0947
\n[\u091a\u0942\u0901\u0915\u093f \u0938\u092e\u094d\u092e\u0941\u0916 \u092d\u0941\u091c\u093e\u0913\u0902 \u0915\u093e \u092a\u094d\u0930\u0924\u094d\u092f\u0947\u0915 \u092f\u0941\u0917\u094d\u092e \u0938\u092e\u093e\u0902\u0924\u0930 \u0939\u094b \u0924\u094b \u0935\u094b \u0938\u092e\u093e\u0902\u0924\u0930 \u091a\u0924\u0941\u0930\u094d\u092d\u0941\u091c \u0939\u094b\u0924\u093e \u0939\u0948]<\/strong>\u00a0|]
\n\u0938\u092e\u0940\u0915\u0930\u0923 (1) \u0924\u0925\u093e (2) \u0938\u0947
\nAECD \u090f\u0915 \u0938\u092e\u093e\u0902\u0924\u0930 \u091a\u0924\u0941\u0930\u094d\u092d\u0941\u091c \u0939\u0948 |
\n\u2234\u00a0AD = CE ………. (3)\u00a0[\u0938\u092e\u093e\u0902\u0924\u0930 \u091a\u0924\u0941\u0930\u094d\u092d\u0941\u091c AECD \u0915\u0940 \u0938\u092e\u094d\u092e\u0941\u0916 \u092d\u0941\u091c\u093e]<\/strong>
\n\u091c\u092c\u0915\u093f, AD = BC\u00a0 ……….. (4) \u0926\u093f\u092f\u093e \u0939\u0948 |
\n\u0938\u092e\u0940o (3) \u0924\u0925\u093e (4) \u0938\u0947
\nBC = CE
\n\u2234\u00a0\u22202 =\u00a0\u22203\u00a0 …………… (5)\u00a0(\u092c\u0930\u093e\u092c\u0930 \u092d\u0941\u091c\u093e\u0913\u0902 \u0915\u0947 \u0938\u092e\u094d\u092e\u0941\u0916 \u0915\u094b\u0923 … )<\/strong>
\nAB || CD \u0926\u093f\u092f\u093e \u0939\u0948 \u0914\u0930 BC \u090f\u0915 \u0924\u093f\u0930\u094d\u092f\u0915 \u0930\u0947\u0916\u093e \u0939\u0948 |
\n\u2234\u00a0\u22202 =\u00a0\u22205 ………….. (6) [\u0905\u0902\u0924: \u090f\u0915\u093e\u0902\u0924\u0930 \u0915\u094b\u0923]
\n\u0938\u092e\u0940o (5) \u0924\u0925\u093e (6) \u0938\u0947 \u0939\u092e\u0947\u0902 \u092a\u094d\u0930\u093e\u092a\u094d\u0924 \u0939\u094b\u0924\u093e \u0939\u0948 |
\n\u22203 =\u00a0\u22205 ………. (7)
\n\u0905\u092c DBEC \u092e\u0947\u0902,
\n\u092c\u0939\u093f\u0937\u094d\u0915\u094b\u0902\u0923\u00a0\u22201 =\u00a0\u22203 +\u00a0\u22204
\n\u092f\u093e \u22201 =\u00a0\u22205 +\u00a0\u22204\u00a0 \u0938\u092e\u0940o (7) \u0938\u0947
\n\u092f\u093e\u00a0 \u2220B =\u00a0\u2220ECD ………… (8)
\n\u091a\u0942\u0901\u0915\u093f, AECD \u090f\u0915 \u0938\u092e\u093e\u0902\u0924\u0930 \u091a\u0924\u0941\u0930\u094d\u092d\u0941\u091c \u0939\u0948 |
\n\u2234 \u2220A =\u00a0\u2220ECD …………… (9)\u00a0[\u0938\u092e\u093e\u0902\u0924\u0930 \u091a\u0924\u0941\u0930\u094d\u092d\u0941\u091c \u0915\u0947 \u0938\u092e\u094d\u092e\u0941\u0916 \u0915\u094b\u0923]<\/strong>
\n\u0938\u092e\u0940o (8) \u0914\u0930 (9) \u0938\u0947
\n\u2220A =\u00a0\u2220B \u00a0………(10) Proved (i)<\/p>\n

(ii) \u092a\u0941\u0928:,\u00a0\u2220D =\u00a0\u2220E \u00a0[\u0938\u092e\u093e\u0902\u0924\u0930 \u091a\u0924\u0941\u0930\u094d\u092d\u0941\u091c \u0915\u0947 \u0938\u092e\u094d\u092e\u0941\u0916 \u0915\u094b\u0923]<\/strong>
\n\u092f\u093e\u00a0 \u2220D =\u00a0\u22203 ……… (11)
\n\"Class
\n\u0938\u092e\u0940o (7) \u0914\u0930 (11) \u0938\u0947
\n\u2220D =\u00a0\u22205
\n\u092f\u093e \u00a0\u00a0\u00a0\u2220D =\u00a0\u2220C\u00a0 proved(ii)
\n(iii) \u00a0\u00a0 \u0394 ABC \u0914\u0930 \u0394 BAD \u092e\u0947\u0902
\nAD = BC (\u0926\u093f\u092f\u093e \u0939\u0948)
\nAB = AB (\u0909\u092d\u092f\u0928\u093f\u0937\u094d\u0920 \u092d\u0941\u091c\u093e’)
\n\u2220A =\u00a0\u2220B \u0938\u092e\u0940o (10) \u0938\u0947
\n\u0905\u0924: SAS \u0938\u0930\u094d\u0935\u093e\u0902\u0917\u0938\u092e\u0924\u093e \u0928\u093f\u092f\u092e \u0938\u0947
\n\u0394 ABC\u00a0\u2245\u00a0\u0394 BAD
\n(iv)\u00a0\u00a0 \u0935\u093f\u0915\u0930\u094d\u0923 AC = \u0935\u093f\u0915\u0930\u094d\u0923 BD (By CPCT \/\u0938\u0930\u094d\u0935\u093e\u0902\u0917\u0938\u092e \u0924\u094d\u0930\u093f\u092d\u0941\u091c \u0915\u0947 \u0938\u0902\u0917\u0924 \u092d\u093e\u0917)<\/p>\n

\u092a\u094d\u0930\u0936\u094d\u0928\u093e\u0935\u0932\u0940 8.2<\/strong><\/span><\/p>\n

\u00a0<\/strong><\/p>\n

Ex 8.2 Class 9 \u0917\u0923\u093f\u0924\u00a0Q1.\u00a0 ABCD \u090f\u0915 \u091a\u0924\u0941\u0930\u094d\u092d\u0941\u091c \u0939\u0948 \u091c\u093f\u0938\u092e\u0947\u0902 P, Q, R \u0914\u0930 S \u0915\u094d\u0930\u092e\u0936: \u092d\u0941\u091c\u093e\u0913\u0902 AB, BC, CD \u0914\u0930 DA \u0915\u0947 \u092e\u0927\u094d\u092f-\u092c\u093f\u0902\u0926\u0941 \u0939\u0948\u0902 | AC \u0909\u0938\u0915\u093e \u090f\u0915 \u0935\u093f\u0915\u0930\u094d\u0923 \u0939\u0948 | \u0926\u0930\u094d\u0936\u093e\u0907\u090f \u0915\u093f<\/strong>
\n\"NCERT
\n\"Class
\n\u0939\u0932 :<\/strong>
\n\u0926\u093f\u092f\u093e \u0939\u0948 :<\/strong>\u00a0ABCD \u090f\u0915 \u091a\u0924\u0941\u0930\u094d\u092d\u0941\u091c \u0939\u0948 \u091c\u093f\u0938\u092e\u0947\u0902 P, Q, R \u0914\u0930 S \u0915\u094d\u0930\u092e\u0936: \u092d\u0941\u091c\u093e\u0913\u0902 AB, BC, CD \u0914\u0930 DA \u0915\u0947 \u092e\u0927\u094d\u092f-\u092c\u093f\u0902\u0926\u0941 \u0939\u0948\u0902 |
\n\u0938\u093f\u0926\u094d\u0927 \u0915\u0930\u0928\u093e \u0939\u0948 :\u00a0<\/strong>
\n\"9th
\n\u0926\u093f\u092f\u093e \u0939\u0948 :<\/strong>\u00a0ABCD \u090f\u0915 \u091a\u0924\u0941\u0930\u094d\u092d\u0941\u091c \u0939\u0948 \u091c\u093f\u0938\u092e\u0947\u0902 P, Q, R \u0914\u0930 S \u0915\u094d\u0930\u092e\u0936: \u092d\u0941\u091c\u093e\u0913\u0902 AB, BC, CD \u0914\u0930 DA \u0915\u0947 \u092e\u0927\u094d\u092f-\u092c\u093f\u0902\u0926\u0941 \u0939\u0948\u0902 |
\n\u0938\u093f\u0926\u094d\u0927 \u0915\u0930\u0928\u093e \u0939\u0948 :\u00a0<\/strong>
\n\"CBSE
\n\"NCERT
\n\u0926\u093f\u092f\u093e \u0939\u0948 : ABCD \u090f\u0915 \u091a\u0924\u0941\u0930\u094d\u092d\u0941\u091c \u0939\u0948 \u091c\u093f\u0938\u092e\u0947\u0902 P, Q, R \u0914\u0930 S \u0915\u094d\u0930\u092e\u0936: \u092d\u0941\u091c\u093e\u0913\u0902 AB, BC, CD \u0914\u0930 DA \u0915\u0947 \u092e\u0927\u094d\u092f-\u092c\u093f\u0902\u0926\u0941 \u0939\u0948\u0902 |
\n\u0938\u093f\u0926\u094d\u0927 \u0915\u0930\u0928\u093e \u0939\u0948 :
\n(\u092f\u0926\u093f \u0915\u093f\u0938\u0940 \u091a\u0924\u0941\u0930\u094d\u092d\u0941\u091c \u0915\u0947 \u0938\u092e\u094d\u092e\u0941\u0916 \u092d\u0941\u091c\u093e\u0913\u0902 \u0915\u0947 \u090f\u0915 \u092f\u0941\u0917\u094d\u092e \u092e\u0947\u0902 \u0938\u0947 \u0915\u094b\u0908 \u092d\u0940 \u090f\u0915 \u092f\u0941\u0917\u094d\u092e \u092c\u0930\u093e\u092c\u0930 \u0914\u0930 \u0938\u092e\u093e\u0928\u094d\u0924\u0930 \u0939\u094b \u0924\u094b \u0935\u094b \u0938\u092e\u093e\u0928\u094d\u0924\u0930 \u091a\u0924\u0941\u0930\u094d\u092d\u0941\u091c \u0939\u094b\u0924\u093e \u0939\u0948)<\/strong>\u00a0 .
\n\u0907\u0938\u0932\u093f\u090f PQRS \u090f\u0915 \u0938\u092e\u093e\u0928\u094d\u0924\u0930 \u091a\u0924\u0941\u0930\u094d\u092d\u0941\u091c \u0939\u0948 |<\/p>\n

Ex 8.2 Class 9 \u0917\u0923\u093f\u0924\u00a0Q2.\u00a0<\/strong>ABCD\u00a0<\/strong>\u090f\u0915 \u0938\u092e\u091a\u0924\u0941\u0930\u094d\u092d\u0941\u091c \u0939\u0948 \u0914\u0930\u00a0<\/strong>P, Q, R\u00a0<\/strong>\u0914\u0930\u00a0<\/strong>S<\/strong>\u00a0\u0915\u094d\u0930\u092e\u0936\u0903 \u092d\u0941\u091c\u093e\u0913\u0902\u00a0<\/strong>AB, BC, CD\u00a0<\/strong>\u0914\u0930\u00a0<\/strong>DA<\/strong>\u00a0\u0915\u0947 \u092e\u0927\u094d\u092f-\u092c\u093f\u0902\u0926\u0941 \u0939\u0948\u0964 \u0926\u0930\u094d\u0936\u093e\u0907\u090f \u0915\u093f \u091a\u0924\u0941\u0930\u094d\u092d\u0941\u091c\u00a0<\/strong>PQRS<\/strong>\u00a0\u090f\u0915 \u0906\u092f\u0924 \u0939\u0948\u0964<\/strong>
\n\"NCERT
\n\u0939\u0932 :<\/strong>
\n\u0926\u093f\u092f\u093e \u0939\u0948 :<\/strong>\u00a0ABCD \u090f\u0915 \u0938\u092e\u091a\u0924\u0941\u0930\u094d\u092d\u0941\u091c \u0939\u0948 \u0914\u0930 P, Q, R \u0914\u0930 S
\n\u0915\u094d\u0930\u092e\u0936\u0903 \u092d\u0941\u091c\u093e\u0913\u0902 AB, BC, CD \u0914\u0930 DA \u0915\u0947 \u092e\u0927\u094d\u092f-\u092c\u093f\u0902\u0926\u0941 \u0939\u0948\u0964
\n\u0938\u093f\u0926\u094d\u0927 \u0915\u0930\u0928\u093e \u0939\u0948 :<\/strong>
\nPQRS \u090f\u0915 \u0906\u092f\u0924 \u0939\u0948 |
\n\u092a\u094d\u0930\u092e\u093e\u0923 :<\/strong>\u00a0\u0924\u094d\u0930\u093f\u092d\u0941\u091c ADC \u092e\u0947\u0902
\nAD \u0924\u0925\u093e CD \u0915\u093e \u092e\u0927\u094d\u092f\u092c\u093f\u0902\u0926\u0941 \u0915\u094d\u0930\u092e\u0936: S \u0924\u0925\u093e R \u0939\u0948 |\u00a0(\u0926\u093f\u092f\u093e \u0939\u0948 )<\/strong>
\n\"Maths
\n(\u092f\u0926\u093f \u0915\u093f\u0938\u0940 \u091a\u0924\u0941\u0930\u094d\u092d\u0941\u091c \u0915\u0947 \u0938\u092e\u094d\u092e\u0941\u0916 \u092d\u0941\u091c\u093e\u0913\u0902 \u0915\u0947 \u090f\u0915 \u092f\u0941\u0917\u094d\u092e \u092e\u0947\u0902 \u0938\u0947 \u0915\u094b\u0908 \u092d\u0940 \u090f\u0915 \u092f\u0941\u0917\u094d\u092e \u092c\u0930\u093e\u092c\u0930 \u0914\u0930 \u0938\u092e\u093e\u0928\u094d\u0924\u0930 \u0939\u094b \u0924\u094b \u0935\u094b \u0938\u092e\u093e\u0928\u094d\u0924\u0930 \u091a\u0924\u0941\u0930\u094d\u092d\u0941\u091c \u0939\u094b\u0924\u093e \u0939\u0948)<\/strong>
\n\u0907\u0938\u0932\u093f\u090f PQRS \u090f\u0915 \u0938\u092e\u093e\u0928\u094d\u0924\u0930 \u091a\u0924\u0941\u0930\u094d\u092d\u0941\u091c \u0939\u0948 |
\n\"Class
\n\u091a\u0942\u0901\u0915\u093f ABCD \u090f\u0915 \u0938\u092e\u091a\u0924\u0941\u0930\u094d\u092d\u0941\u091c \u0939\u0948 |
\n\u0907\u0938\u0932\u093f\u090f,\u00a0\u2220AOD = 90\u0966<\/sup>
\n\u092f\u093e\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u2220MON = 90\u0966<\/sup>
\n(\u0938\u092e\u091a\u0924\u0941\u0930\u094d\u092d\u0941\u091c \u0915\u0947 \u0935\u093f\u0915\u0930\u094d\u0923 \u090f\u0915 \u0926\u0941\u0938\u0930\u0947 \u0915\u094b \u0938\u092e\u0915\u094b\u0923 \u092a\u0930 \u0938\u092e\u0926\u094d\u0935\u093f\u092d\u093e\u091c\u093f\u0924 \u0915\u0930\u0924\u0947 \u0939\u0948\u0902 !)
\n\u0905\u092c\u00a0 SR || AC \u0914\u0930 SP || BD \u0939\u0948
\n\u0924\u094b\u00a0\u00a0 SMON \u092d\u0940 \u090f\u0915 \u0938\u092e\u093e\u0928\u094d\u0924\u0930 \u091a\u0924\u0941\u0930\u094d\u092d\u0941\u091c \u0939\u0948 |
\n\u0907\u0938\u0932\u093f\u090f\u00a0\u2220MSN =\u00a0\u2220MON = 90\u0966<\/sup>\u00a0(\u0938\u092e\u093e\u0902\u0924\u0930 \u091a\u0924\u0941\u0930\u094d\u092d\u0941\u091c \u0915\u0947 \u0938\u092e\u094d\u092e\u0941\u0916 \u0915\u094b\u0923 \u092c\u0930\u093e\u092c\u0930 \u0939\u094b\u0924\u0947 \u0939\u0948\u0902)
\n\u092f\u093e\u00a0\u00a0\u00a0\u00a0\u00a0\u2220PSR = 90\u0966<\/sup>
\n\u0905\u0924: PQRS \u090f\u0915 \u0906\u092f\u0924 \u0939\u0948 |
\nProved.<\/p>\n

Ex 8.2 Class 9 \u0917\u0923\u093f\u0924\u00a0Q3. ABCD \u090f\u0915 \u0906\u092f\u0924 \u0939\u0948, \u091c\u093f\u0938\u092e\u0947\u0902 P, Q, R \u0914\u0930 S \u0915\u094d\u0930\u092e\u0936: \u092d\u0941\u091c\u093e\u0913\u0902 AB, BC, CD \u0914\u0930 DA \u0915\u0947 \u092e\u0927\u094d\u092f-\u092c\u093f\u0902\u0926\u0941 \u0939\u0948\u0902 | \u0926\u0930\u094d\u0936\u093e\u0907\u090f \u0915\u093f \u091a\u0924\u0941\u0930\u094d\u092d\u0941\u091c PQRS \u090f\u0915 \u0938\u092e\u091a\u0924\u0941\u0930\u094d\u092d\u0941\u091c \u0939\u0948|<\/strong>
\n\"NCERT
\n\u0939\u0932 :<\/strong>
\n\u0926\u093f\u092f\u093e \u0939\u0948 :<\/strong>\u00a0ABCD \u090f\u0915 \u0906\u092f\u0924 \u0939\u0948, \u091c\u093f\u0938\u092e\u0947\u0902 P, Q, R \u0914\u0930 S \u0915\u094d\u0930\u092e\u0936: \u092d\u0941\u091c\u093e\u0913\u0902 AB, BC, CD \u0914\u0930 DA \u0915\u0947 \u092e\u0927\u094d\u092f-\u092c\u093f\u0902\u0926\u0941 \u0939\u0948\u0902 |
\n\u0938\u093f\u0926\u094d\u0927 \u0915\u0930\u0928\u093e \u0939\u0948 :<\/strong>
\nPQRS \u090f\u0915 \u0938\u092e\u091a\u0924\u0941\u0930\u094d\u092d\u0941\u091c \u0939\u0948 |
\n\u0930\u091a\u0928\u093e :<\/strong>\u00a0A \u0915\u094b C \u0938\u0947 \u092e\u093f\u0932\u093e\u092f\u093e |
\n\u092a\u094d\u0930\u092e\u093e\u0923 :<\/strong>\u00a0\u0924\u094d\u0930\u093f\u092d\u0941\u091c ADC \u092e\u0947\u0902
\nAD \u0924\u0925\u093e CD \u0915\u093e \u092e\u0927\u094d\u092f\u092c\u093f\u0902\u0926\u0941 \u0915\u094d\u0930\u092e\u0936: S \u0924\u0925\u093e R \u0939\u0948 |\u00a0(\u0926\u093f\u092f\u093e \u0939\u0948 )<\/strong>
\n\u0905\u0924: \u092e\u0927\u094d\u092f-\u092c\u093f\u0902\u0926\u0941 \u092a\u094d\u0930\u092e\u0947\u092f \u0938\u0947
\n\"NCERT
\n(\u092f\u0926\u093f \u0915\u093f\u0938\u0940 \u091a\u0924\u0941\u0930\u094d\u092d\u0941\u091c \u0915\u0947 \u0938\u092e\u094d\u092e\u0941\u0916 \u092d\u0941\u091c\u093e\u0913\u0902 \u0915\u0947 \u090f\u0915 \u092f\u0941\u0917\u094d\u092e \u092e\u0947\u0902 \u0938\u0947 \u0915\u094b\u0908 \u092d\u0940 \u090f\u0915 \u092f\u0941\u0917\u094d\u092e \u092c\u0930\u093e\u092c\u0930 \u0914\u0930 \u0938\u092e\u093e\u0928\u094d\u0924\u0930 \u0939\u094b \u0924\u094b \u0935\u094b \u0938\u092e\u093e\u0928\u094d\u0924\u0930 \u091a\u0924\u0941\u0930\u094d\u092d\u0941\u091c \u0939\u094b\u0924\u093e \u0939\u0948)<\/strong>\u00a0 .
\n\u0907\u0938\u0932\u093f\u090f PQRS \u090f\u0915 \u0938\u092e\u093e\u0928\u094d\u0924\u0930 \u091a\u0924\u0941\u0930\u094d\u092d\u0941\u091c \u0939\u0948 |
\n\"Maths
\n\u0905\u092c, \u091a\u0942\u0901\u0915\u093f ABCD \u090f\u0915 \u0906\u092f\u0924 \u0939\u0948 |
\n\u0907\u0938\u0932\u093f\u090f ,\u00a0 AB || CD\u00a0 \u092f\u093e\u00a0 SQ || CD\u00a0 …(i)
\n(\u0915\u094d\u092f\u094b\u0902\u0915\u093f S \u0924\u0925\u093e Q AD \u0924\u0925\u093e BC \u0915\u0947 \u092e\u0927\u094d\u092f-\u092c\u093f\u0902\u0926\u0941 \u0939\u0948 |)
\n\u0907\u0938\u0940\u092a\u094d\u0930\u0915\u093e\u0930 AD || PR\u00a0 …… (ii)
\n\u0905\u0924: \u0938\u092e\u0940\u0915\u0930\u0923 (i) \u0924\u0925\u093e (ii) \u0938\u0947
\nDSOR \u090f\u0915 \u0938\u092e\u093e\u0928\u094d\u0924\u0930 \u091a\u0924\u0941\u0930\u094d\u092d\u0941\u091c \u0939\u0948 |
\n\u0907\u0938\u0932\u093f\u090f,\u00a0\u2220SOR =\u00a0\u2220D\u00a0 (\u0938\u092e\u093e\u0928\u094d\u0924\u0930 \u091a\u0924\u0941\u0930\u094d\u092d\u0941\u091c \u0915\u093f \u0938\u092e\u094d\u092e\u0941\u0916 \u092d\u0941\u091c\u093e)
\n\u091c\u092c\u0915\u093f,\u00a0\u2220D = 90\u0966<\/sup>\u00a0 (\u0906\u092f\u0924 \u0915\u093e \u092a\u094d\u0930\u0924\u094d\u092f\u0947\u0915 \u0915\u094b\u0923)
\n\u0907\u0938\u0932\u093f\u090f\u00a0\u2220SOR = 90\u0966<\/sup>
\n\u091a\u0942\u0901\u0915\u093f PQRS \u090f\u0915 \u0938\u092e\u093e\u0902\u0924\u0930 \u091a\u0924\u0941\u0930\u094d\u092d\u0941\u091c \u0939\u0948 \u091c\u093f\u0938\u0915\u0947 \u0935\u093f\u0915\u0930\u094d\u0923 \u0938\u092e\u0915\u094b\u0923 \u092a\u0930 \u092a\u094d\u0930\u0924\u093f\u091a\u094d\u091b\u0947\u0926 \u0915\u0930\u0924\u0947 \u0939\u0948\u0902 |
\n\u0905\u0924: PQRS \u090f\u0915 \u0938\u092e\u091a\u0924\u0941\u0930\u094d\u092d\u0941\u091c \u0939\u0948 |
\n(\u0935\u0939 \u0938\u092e\u093e\u0902\u0924\u0930 \u091a\u0924\u0941\u0930\u094d\u092d\u0941\u091c \u091c\u093f\u0938\u0915\u0947 \u0935\u093f\u0915\u0930\u094d\u0923 \u0938\u092e\u0915\u094b\u0923 \u092a\u0930 \u092a\u094d\u0930\u0924\u093f\u091a\u094d\u091b\u0947\u0926 \u0915\u0930\u0924\u0947 \u0939\u0948\u0902 \u0938\u092e\u091a\u0924\u0941\u0930\u094d\u092d\u0941\u091c \u0915\u0939\u0932\u093e\u0924\u093e \u0939\u0948 |)<\/p>\n

Ex 8.2 Class 9 \u0917\u0923\u093f\u0924\u00a0Q4.\u00a0<\/strong>ABCD<\/strong>\u00a0\u090f\u0915 \u0938\u092e\u0932\u0902\u092c \u0939\u0948<\/strong>, \u091c\u093f\u0938\u092e\u0947\u0902 AB || DC \u0939\u0948\u0964 \u0938\u093e\u0925 \u0939\u0940, BD \u090f\u0915 \u0935\u093f\u0915\u0930\u094d\u0923 \u0939\u0948 \u0914\u0930 E \u092d\u0941\u091c\u093e AD \u0915\u093e \u092e\u0927\u094d\u092f-\u092c\u093f\u0902\u0926\u0941 \u0939\u0948\u0964 E \u0938\u0947 \u0939\u094b\u0915\u0930 \u090f\u0915 \u0930\u0947\u0916\u093e AB \u0915\u0947 \u0938\u092e\u093e\u0902\u0924\u0930 \u0916\u0940\u0902\u091a\u0940 \u0917\u0908 \u0939\u0948, \u091c\u094b BC \u0915\u094b F \u092a\u0930 \u092a\u094d\u0930\u0924\u093f\u091a\u094d\u091b\u0947\u0926 \u0915\u0930\u0924\u0940 \u0939\u0948 \u0964 \u0926\u0930\u094d\u0936\u093e\u0907\u090f \u0915\u093f F \u092d\u0941\u091c\u093e BC \u0915\u093e \u092e\u0927\u094d\u092f-\u092c\u093f\u0902\u0926\u0941 \u0939\u0948\u0964
\n\"Class
\n\u0939\u0932 :\u00a0<\/strong><\/strong>
\n\u0926\u093f\u092f\u093e \u0939\u0948 :<\/strong>\u00a0ABCD \u090f\u0915 \u0938\u092e\u0932\u0902\u092c \u0939\u0948, \u091c\u093f\u0938\u092e\u0947\u0902 AB || DC \u0939\u0948\u0964
\n\u0938\u093e\u0925 \u0939\u0940, BD \u090f\u0915 \u0935\u093f\u0915\u0930\u094d\u0923 \u0939\u0948 \u0914\u0930 E \u092d\u0941\u091c\u093e AD \u0915\u093e
\n\u092e\u0927\u094d\u092f-\u092c\u093f\u0902\u0926\u0941 \u0939\u0948\u0964 E \u0938\u0947 \u0939\u094b\u0915\u0930 \u090f\u0915 \u0930\u0947\u0916\u093e AB \u0915\u0947 \u0938\u092e\u093e\u0902\u0924\u0930
\n\u0916\u0940\u0902\u091a\u0940 \u0917\u0908 \u0939\u0948, \u091c\u094b BC \u0915\u094b F \u092a\u0930 \u092a\u094d\u0930\u0924\u093f\u091a\u094d\u091b\u0947\u0926 \u0915\u0930\u0924\u0940 \u0939\u0948 \u0964
\n\u0938\u093f\u0926\u094d\u0927 \u0915\u0930\u0928\u093e \u0939\u0948 :<\/strong>\u00a0CF = BF
\n\u0930\u091a\u0928\u093e :<\/strong>\u00a0D \u0915\u094b B \u0938\u0947 \u092e\u093f\u0932\u093e\u092f\u093e \u091c\u094b EF \u0915\u094b G \u092a\u0930 \u092a\u094d\u0930\u0924\u093f\u091a\u094d\u091b\u0947\u0926 \u0915\u0930\u0924\u093e \u0939\u0948 |
\n\u092a\u094d\u0930\u092e\u093e\u0923 :<\/strong>
\nDABD \u092e\u0947\u0902,
\nAB || EF ….. (i) (\u0926\u093f\u092f\u093e \u0939\u0948)
\n\u0914\u0930 E \u092d\u0941\u091c\u093e AD \u0915\u093e \u092e\u0927\u094d\u092f-\u092c\u093f\u0902\u0926\u0941 \u0939\u0948|
\n(\u0915\u093f\u0938\u0940 \u0924\u094d\u0930\u093f\u092d\u0941\u091c \u0915\u0940 \u090f\u0915 \u092d\u0941\u091c\u093e \u0915\u0947 \u092e\u0927\u094d\u092f-\u092c\u093f\u0902\u0926\u0941 \u0938\u0947 \u0926\u0942\u0938\u0930\u0940 \u092d\u0941\u091c\u093e \u0915\u0947 \u0938\u092e\u093e\u0902\u0924\u0930 \u0916\u093f\u0902\u091a\u0940 \u0917\u0908 \u0930\u0947\u0916\u093e \u0924\u0940\u0938\u0930\u0940 \u092d\u0941\u091c\u093e \u0915\u094b \u0938\u092e\u0926\u094d\u0935\u093f\u092d\u093e\u091c\u093f\u0924 \u0915\u0930\u0924\u0940 \u0939\u0948)
\n\u0905\u0924: \u092e\u0927\u094d\u092f-\u092c\u093f\u0902\u0926\u0941 \u092a\u094d\u0930\u092e\u0947\u092f 8.10 \u0938\u0947
\n\u0907\u0938\u0932\u093f\u090f \u092c\u093f\u0902\u0926\u0941 G \u092d\u0941\u091c\u093e BD \u0915\u093e \u092e\u0927\u094d\u092f-\u092c\u093f\u0902\u0926\u0941 \u0939\u0948| …. (i)
\n\u0905\u092c\u00a0\u00a0 AB || CD\u00a0\u00a0 ……. (ii) (\u0926\u093f\u092f\u093e \u0939\u0948)
\n\u0938\u092e\u0940\u0915\u0930\u0923 (i) \u0924\u0925\u093e (ii) \u0938\u0947
\nCD || EF \u0914\u0930 \u092c\u093f\u0902\u0926\u0941 G \u092d\u0941\u091c\u093e BD \u0915\u093e \u092e\u0927\u094d\u092f-\u092c\u093f\u0902\u0926\u0941 \u0939\u0948\u00a0 [\u0938\u092e\u0940\u0915\u0930\u0923 (i) \u0938\u0947]
\n\u0905\u0924: \u092e\u0927\u094d\u092f-\u092c\u093f\u0902\u0926\u0941 \u092a\u094d\u0930\u092e\u0947\u092f 8.10 \u0938\u0947 DBCD \u092e\u0947\u0902
\nF \u092d\u0941\u091c\u093e BC \u0915\u093e \u092e\u0927\u094d\u092f-\u092c\u093f\u0902\u0926\u0941 \u0939\u0948 |
\n\u0907\u0938\u0932\u093f\u090f\u00a0 CF = BF
\nproved.<\/p>\n

Ex 8.2 Class 9 \u0917\u0923\u093f\u0924\u00a0Q5. \u090f\u0915 \u0938\u092e\u093e\u0902\u0924\u0930 \u091a\u0924\u0941\u0930\u094d\u092d\u0941\u091c ABCD \u092e\u0947\u0902 E \u0914\u0930 F \u0915\u094d\u0930\u092e\u0936: \u092d\u0941\u091c\u093e\u0913\u0902 AB \u0914\u0930 CD \u0915\u0947 \u092e\u0927\u094d\u092f-\u092c\u093f\u0902\u0926\u0941 \u0939\u0948\u0902 |\u00a0<\/strong>\u0926\u0930\u094d\u0936\u093e\u0907\u090f \u0915\u093f \u0930\u0947\u0916\u093e\u0916\u0902\u0921 AF \u0914\u0930 EC \u0935\u093f\u0915\u0930\u094d\u0923 BD \u0915\u094b \u0938\u092e\u0924\u094d\u0930\u093f\u092d\u093e\u091c\u093f\u0924 \u0915\u0930\u0924\u0947 \u0939\u0948\u0902 |<\/strong>
\n\"NCERT
\n\u0939\u0932 :<\/strong>
\n\u0926\u093f\u092f\u093e \u0939\u0948 :<\/strong>\u00a0\u090f\u0915 \u0938\u092e\u093e\u0902\u0924\u0930 \u091a\u0924\u0941\u0930\u094d\u092d\u0941\u091c ABCD \u092e\u0947\u0902 E \u0914\u0930 F
\n\u0915\u094d\u0930\u092e\u0936: \u092d\u0941\u091c\u093e\u0913\u0902 AB \u0914\u0930 CD \u0915\u0947 \u092e\u0927\u094d\u092f-\u092c\u093f\u0902\u0926\u0941 \u0939\u0948\u0902 |
\n\u0938\u093f\u0926\u094d\u0927 \u0915\u0930\u0928\u093e \u0939\u0948 :<\/strong>\u00a0DP = PQ = QB
\n\u092a\u094d\u0930\u092e\u093e\u0923 :<\/strong>
\nDABP \u092e\u0947\u0902,
\nE \u092d\u0941\u091c\u093e AB \u0915\u093e \u092e\u0927\u094d\u092f-\u092c\u093f\u0902\u0926\u0941 \u0939\u0948 \u0914\u0930 AF||EC \u0926\u093f\u092f\u093e \u0939\u0948 |
\n\u0905\u0924: \u092e\u0927\u094d\u092f-\u092c\u093f\u0902\u0926\u0941 \u092a\u094d\u0930\u092e\u0947\u092f 8.10 \u0938\u0947
\nQ \u092d\u0941\u091c\u093e PB \u0915\u093e \u092e\u0927\u094d\u092f-\u092c\u093f\u0902\u0926\u0941 \u0939\u0948 |
\n\u0905\u0924: PQ = QB\u00a0 ………. (i)
\n(\u0915\u093f\u0938\u0940 \u0924\u094d\u0930\u093f\u092d\u0941\u091c \u0915\u0940 \u090f\u0915 \u092d\u0941\u091c\u093e \u0915\u0947 \u092e\u0927\u094d\u092f-\u092c\u093f\u0902\u0926\u0941 \u0938\u0947 \u0926\u0942\u0938\u0930\u0940 \u092d\u0941\u091c\u093e \u0915\u0947 \u0938\u092e\u093e\u0902\u0924\u0930 \u0916\u093f\u0902\u091a\u0940 \u0917\u0908 \u0930\u0947\u0916\u093e \u0924\u0940\u0938\u0930\u0940 \u092d\u0941\u091c\u093e \u0915\u094b \u0938\u092e\u0926\u094d\u0935\u093f\u092d\u093e\u091c\u093f\u0924 \u0915\u0930\u0924\u0940 \u0939\u0948)
\n\u0905\u092c, DCDQ \u092e\u0947\u0902,
\nF \u092d\u0941\u091c\u093e CD \u0915\u093e \u092e\u0927\u094d\u092f-\u092c\u093f\u0902\u0926\u0941 \u0939\u0948 \u0914\u0930 AF||EC \u0926\u093f\u092f\u093e \u0939\u0948 |
\n\u0905\u0924: \u092e\u0927\u094d\u092f-\u092c\u093f\u0902\u0926\u0941 \u092a\u094d\u0930\u092e\u0947\u092f 8.10 \u0938\u0947
\nP \u092d\u0941\u091c\u093e DQ \u0915\u093e \u092e\u0927\u094d\u092f-\u092c\u093f\u0902\u0926\u0941 \u0939\u0948 |
\n\u0907\u0938\u0932\u093f\u090f,\u00a0 DP = PQ\u00a0\u00a0\u00a0 …….. (ii)
\n\u0938\u092e\u0940\u0915\u0930\u0923 (i) \u0924\u0925\u093e (ii) \u0938\u0947
\nDP = PQ = QB
\nProved.<\/p>\n

Ex 8.2 Class 9 \u0917\u0923\u093f\u0924\u00a0Q6.\u00a0<\/strong>\u0926\u0930\u094d\u0936\u093e\u0907\u090f \u0915\u093f \u0915\u093f\u0938\u0940 \u091a\u0924\u0941\u0930\u094d\u092d\u0941\u091c \u0915\u0940 \u0938\u092e\u094d\u092e\u0941\u0916 \u092d\u0941\u091c\u093e\u0913\u0902 \u0915\u0947 \u092e\u0927\u094d\u092f-\u092c\u093f\u0902\u0926\u0941\u0913\u0902 \u0915\u094b \u092e\u093f\u0932\u093e\u0928\u0947 \u0935\u093e\u0932\u0947 \u0930\u0947\u0916\u093e\u0916\u0902\u0921\u00a0<\/strong>\u092a\u0930\u0938\u094d\u092a\u0930 \u0938\u092e\u0926\u094d\u0935\u093f\u092d\u093e\u091c\u093f\u0924 \u0915\u0930\u0924\u0947 \u0939\u0948\u0902\u0964<\/strong>
\n\"NCERT
\n\u0939\u0932 :<\/strong>
\n\u0926\u093f\u092f\u093e \u0939\u0948 :<\/strong>\u00a0ABCD \u090f\u0915 \u091a\u0924\u0941\u0930\u094d\u092d\u0941\u091c \u0939\u0948 \u091c\u093f\u0938\u0915\u0947 \u092d\u0941\u091c\u093e\u090f\u0901
\nAB, BC, CD \u0914\u0930 DA \u0915\u093e \u092e\u0927\u094d\u092f-\u092c\u093f\u0902\u0926\u0941 \u0915\u094d\u0930\u092e\u0936:
\nP, Q, R \u0914\u0930 S \u0939\u0948 |
\n\u0938\u093f\u0926\u094d\u0927 \u0915\u0930\u0928\u093e \u0939\u0948 :<\/strong>\u00a0\u0935\u093f\u0915\u0930\u094d\u0923 PR \u0914\u0930 SQ \u090f\u0915 \u0926\u0941\u0938\u0930\u0947 \u0915\u094b \u0938\u092e\u0926\u094d\u0935\u093f\u092d\u093e\u091c\u093f\u0924 \u0915\u0930\u0924\u0947 \u0939\u0948\u0902 |
\n\u0930\u091a\u0928\u093e :<\/strong>\u00a0P, Q, R \u0914\u0930 S \u0915\u094b \u092e\u093f\u0932\u093e\u092f\u093e \u0914\u0930 A \u0915\u094b C \u0938\u0947 \u092e\u093f\u0932\u093e\u092f\u093e |
\n\"NCERT
\n(\u092f\u0926\u093f \u0915\u093f\u0938\u0940 \u091a\u0924\u0941\u0930\u094d\u092d\u0941\u091c \u0915\u0947 \u0938\u092e\u094d\u092e\u0941\u0916 \u092d\u0941\u091c\u093e\u0913\u0902 \u0915\u0947 \u090f\u0915 \u092f\u0941\u0917\u094d\u092e \u092e\u0947\u0902 \u0938\u0947 \u0915\u094b\u0908 \u092d\u0940 \u090f\u0915 \u092f\u0941\u0917\u094d\u092e \u092c\u0930\u093e\u092c\u0930 \u0914\u0930 \u0938\u092e\u093e\u0928\u094d\u0924\u0930 \u0939\u094b \u0924\u094b \u0935\u094b \u0938\u092e\u093e\u0928\u094d\u0924\u0930 \u091a\u0924\u0941\u0930\u094d\u092d\u0941\u091c \u0939\u094b\u0924\u093e \u0939\u0948)<\/strong>\u00a0 .
\n\u0907\u0938\u0932\u093f\u090f PQRS \u090f\u0915 \u0938\u092e\u093e\u0928\u094d\u0924\u0930 \u091a\u0924\u0941\u0930\u094d\u092d\u0941\u091c \u0939\u0948 |
\n\u0905\u092c \u091a\u0942\u0901\u0915\u093f PQRS \u090f\u0915 \u0938\u092e\u093e\u0902\u0924\u0930 \u091a\u0924\u0941\u0930\u094d\u092d\u0941\u091c \u0939\u0948 \u0924\u094b \u0907\u0938\u0915\u0947 \u0935\u093f\u0915\u0930\u094d\u0923 PR \u0914\u0930 SQ \u090f\u0915 \u0926\u0941\u0938\u0930\u0947 \u0915\u094b \u0938\u092e\u0926\u094d\u0935\u093f\u092d\u093e\u091c\u093f\u0924 \u0915\u0930\u0924\u0947 \u0939\u0948\u0902 |
\n(\u0938\u092e\u093e\u0902\u0924\u0930 \u091a\u0924\u0941\u0930\u094d\u092d\u0941\u091c \u0915\u0947 \u0935\u093f\u0915\u0930\u094d\u0923 \u090f\u0915 \u0926\u0941\u0938\u0930\u0947 \u0915\u094b \u0938\u092e\u0926\u094d\u0935\u093f\u092d\u093e\u091c\u093f\u0924 \u0915\u0930\u0924\u0947 \u0939\u0948 |)<\/p>\n

Ex 8.2 Class 9 \u0917\u0923\u093f\u0924\u00a0Q7. ABC \u090f\u0915 \u0924\u094d\u0930\u093f\u092d\u0941\u091c \u0939\u0948 \u091c\u093f\u0938\u0915\u093e \u0915\u094b\u0923 C \u0938\u092e\u0915\u094b\u0923 \u0939\u0948 | \u0915\u0930\u094d\u0923 AB \u0915\u0947 \u092e\u0927\u094d\u092f-\u092c\u093f\u0902\u0926\u0941 M \u0938\u0947 \u0939\u094b\u0915\u0930 BC \u0915\u0947 \u0938\u092e\u093e\u0902\u0924\u0930 \u0916\u093f\u0902\u091a\u0940 \u0917\u0908 \u0930\u0947\u0916\u093e AC \u0915\u094b D \u092a\u0930 \u092a\u094d\u0930\u0924\u093f\u091a\u094d\u091b\u0947\u0926 \u0915\u0930\u0924\u0940 \u0939\u0948 | \u0926\u0930\u094d\u0936\u093e\u0907\u090f \u0915\u093f\u00a0<\/strong>
\n\"NCERT
\n\"NCERT
\n\u0939\u0932 :<\/strong>
\n\u0926\u093f\u092f\u093e \u0939\u0948 :<\/strong>\u00a0ABC \u090f\u0915 \u0924\u094d\u0930\u093f\u092d\u0941\u091c \u0939\u0948 \u091c\u093f\u0938\u0915\u093e
\n\u0915\u094b\u0923 C \u0938\u092e\u0915\u094b\u0923 \u0939\u0948 | \u0915\u0930\u094d\u0923 AB \u0915\u0947 \u092e\u0927\u094d\u092f-\u092c\u093f\u0902\u0926\u0941
\nM \u0938\u0947 \u0939\u094b\u0915\u0930 BC \u0915\u0947 \u0938\u092e\u093e\u0902\u0924\u0930 \u0916\u093f\u0902\u091a\u0940 \u0917\u0908 \u0930\u0947\u0916\u093e
\nAC \u0915\u094b D \u092a\u0930 \u092a\u094d\u0930\u0924\u093f\u091a\u094d\u091b\u0947\u0926 \u0915\u0930\u0924\u0940 \u0939\u0948 |
\n\u0938\u093f\u0926\u094d\u0927 \u0915\u0930\u0928\u093e \u0939\u0948 :\u00a0<\/strong>
\n\"Maths
\n\u092a\u094d\u0930\u092e\u093e\u0923 :<\/strong>\u00a0(i)\u00a0 DABC \u092e\u0947\u0902
\nM \u092d\u0941\u091c\u093e AB \u0915\u093e \u092e\u0927\u094d\u092f-\u092c\u093f\u0902\u0926\u0941 \u0939\u0948 \u0914\u0930 MD || BC \u0939\u0948 |
\n\u0905\u0924: \u092e\u0927\u094d\u092f-\u092c\u093f\u0902\u0926\u0941 \u092a\u094d\u0930\u092e\u0947\u092f 8.10 \u0938\u0947
\n(\u0915\u093f\u0938\u0940 \u0924\u094d\u0930\u093f\u092d\u0941\u091c \u0915\u0940 \u090f\u0915 \u092d\u0941\u091c\u093e \u0915\u0947 \u092e\u0927\u094d\u092f-\u092c\u093f\u0902\u0926\u0941 \u0938\u0947 \u0926\u0942\u0938\u0930\u0940 \u092d\u0941\u091c\u093e \u0915\u0947 \u0938\u092e\u093e\u0902\u0924\u0930 \u0916\u093f\u0902\u091a\u0940 \u0917\u0908 \u0930\u0947\u0916\u093e \u0924\u0940\u0938\u0930\u0940 \u092d\u0941\u091c\u093e \u0915\u094b \u0938\u092e\u0926\u094d\u0935\u093f\u092d\u093e\u091c\u093f\u0924 \u0915\u0930\u0924\u0940 \u0939\u0948)
\n\u0907\u0938\u0932\u093f\u090f, D \u092d\u0941\u091c\u093e AC \u0915\u093e \u092e\u0927\u094d\u092f-\u092c\u093f\u0902\u0926\u0941 \u0939\u0948 |
\n\u0905\u0924: AD = CD …….. (i)
\n(ii)\u00a0 MD || BC \u0926\u093f\u092f\u093e \u0939\u0948 \u0914\u0930 AC \u090f\u0915 \u0924\u093f\u0930\u094d\u092f\u0915 \u0930\u0947\u0916\u093e \u0939\u0948 |
\n\"Maths<\/p>\n

Hope given NCERT Solutions for Class 9 Maths Chapter 8 are helpful to complete your homework.<\/p>\n","protected":false},"excerpt":{"rendered":"

NCERT Solutions for Class 9 Maths Chapter 8 Quadrilaterals (\u091a\u0924\u0941\u0930\u094d\u092d\u0941\u091c) (Hindi Medium) These Solutions are part of NCERT Solutions for Class 9 Maths in Hindi Medium. Here we have given NCERT Solutions for Class 9 Maths Chapter 8 Quadrilaterals. \u092a\u094d\u0930\u0936\u094d\u0928\u093e\u0935\u0932\u0940 8.1\u00a0 Ex 8.1 Class 9 \u0917\u0923\u093f\u0924 Q1. \u090f\u0915 \u091a\u0924\u0941\u0930\u094d\u092d\u0941\u091c \u0915\u0947 \u0915\u094b\u0923 3 : 5 : …<\/p>\n

NCERT Solutions for Class 9 Maths Chapter 8 Quadrilaterals (Hindi Medium)<\/span> Read More »<\/a><\/p>\n","protected":false},"author":9,"featured_media":7723,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"site-sidebar-layout":"default","site-content-layout":"default","ast-main-header-display":"","ast-hfb-above-header-display":"","ast-hfb-below-header-display":"","ast-hfb-mobile-header-display":"","site-post-title":"","ast-breadcrumbs-content":"","ast-featured-img":"","footer-sml-layout":"","theme-transparent-header-meta":"default","adv-header-id-meta":"","stick-header-meta":"default","header-above-stick-meta":"","header-main-stick-meta":"","header-below-stick-meta":"","spay_email":""},"categories":[6],"tags":[],"yoast_head":"\nNCERT Solutions for Class 9 Maths Chapter 8 Quadrilaterals (Hindi Medium) - MCQ Questions<\/title>\n<meta name=\"robots\" content=\"index, follow, max-snippet:-1, max-image-preview:large, max-video-preview:-1\" \/>\n<link rel=\"canonical\" href=\"https:\/\/mcq-questions.com\/ncert-solutions-for-class-9-maths-chapter-8-hindi\/\" \/>\n<meta property=\"og:locale\" content=\"en_US\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"NCERT Solutions for Class 9 Maths Chapter 8 Quadrilaterals (Hindi Medium) - MCQ Questions\" \/>\n<meta property=\"og:description\" content=\"NCERT Solutions for Class 9 Maths Chapter 8 Quadrilaterals (\u091a\u0924\u0941\u0930\u094d\u092d\u0941\u091c) (Hindi Medium) These Solutions are part of NCERT Solutions for Class 9 Maths in Hindi Medium. 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Here we have given NCERT Solutions for Class 9 Maths Chapter 8 Quadrilaterals. \u092a\u094d\u0930\u0936\u094d\u0928\u093e\u0935\u0932\u0940 8.1\u00a0 Ex 8.1 Class 9 \u0917\u0923\u093f\u0924 Q1. \u090f\u0915 \u091a\u0924\u0941\u0930\u094d\u092d\u0941\u091c \u0915\u0947 \u0915\u094b\u0923 3 : 5 : … NCERT Solutions for Class 9 Maths Chapter 8 Quadrilaterals (Hindi Medium) Read More »","og_url":"https:\/\/mcq-questions.com\/ncert-solutions-for-class-9-maths-chapter-8-hindi\/","og_site_name":"MCQ Questions","article_publisher":"https:\/\/www.facebook.com\/NCERTSolutionsGuru\/","article_published_time":"2021-07-23T10:30:38+00:00","article_modified_time":"2022-03-02T04:53:19+00:00","og_image":[{"width":1280,"height":720,"url":"https:\/\/mcq-questions.com\/wp-content\/uploads\/2019\/09\/NCERT-Solutions-for-Class-9-Maths-Chapter-8-Quadrilaterals-Hindi-Medium.png","type":"image\/png"}],"twitter_card":"summary_large_image","twitter_creator":"@ncertsolguru","twitter_site":"@ncertsolguru","twitter_misc":{"Written by":"Prasanna","Est. reading time":"6 minutes"},"schema":{"@context":"https:\/\/schema.org","@graph":[{"@type":"WebSite","@id":"https:\/\/mcq-questions.com\/#website","url":"https:\/\/mcq-questions.com\/","name":"MCQ Questions","description":"MCQ Questions for Class 1 to 12","potentialAction":[{"@type":"SearchAction","target":{"@type":"EntryPoint","urlTemplate":"https:\/\/mcq-questions.com\/?s={search_term_string}"},"query-input":"required name=search_term_string"}],"inLanguage":"en-US"},{"@type":"ImageObject","@id":"https:\/\/mcq-questions.com\/ncert-solutions-for-class-9-maths-chapter-8-hindi\/#primaryimage","inLanguage":"en-US","url":"https:\/\/i2.wp.com\/mcq-questions.com\/wp-content\/uploads\/2019\/09\/NCERT-Solutions-for-Class-9-Maths-Chapter-8-Quadrilaterals-Hindi-Medium.png?fit=1280%2C720&ssl=1","contentUrl":"https:\/\/i2.wp.com\/mcq-questions.com\/wp-content\/uploads\/2019\/09\/NCERT-Solutions-for-Class-9-Maths-Chapter-8-Quadrilaterals-Hindi-Medium.png?fit=1280%2C720&ssl=1","width":1280,"height":720,"caption":"NCERT Solutions for Class 9 Maths Chapter 8 Quadrilaterals (Hindi Medium)"},{"@type":"WebPage","@id":"https:\/\/mcq-questions.com\/ncert-solutions-for-class-9-maths-chapter-8-hindi\/#webpage","url":"https:\/\/mcq-questions.com\/ncert-solutions-for-class-9-maths-chapter-8-hindi\/","name":"NCERT Solutions for Class 9 Maths Chapter 8 Quadrilaterals (Hindi Medium) - 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