{"id":27876,"date":"2021-07-02T11:33:29","date_gmt":"2021-07-02T06:03:29","guid":{"rendered":"https:\/\/mcq-questions.com\/?p=27876"},"modified":"2022-03-02T10:30:59","modified_gmt":"2022-03-02T05:00:59","slug":"ncert-solutions-for-class-7-maths-chapter-7-intext-questions","status":"publish","type":"post","link":"https:\/\/mcq-questions.com\/ncert-solutions-for-class-7-maths-chapter-7-intext-questions\/","title":{"rendered":"NCERT Solutions for Class 7 Maths Chapter 7 Congruence of Triangles InText Questions"},"content":{"rendered":"

These NCERT Solutions for Class 7 Maths<\/a> Chapter 7 Congruence of Triangles InText Questions and Answers are prepared by our highly skilled subject experts.<\/p>\n

NCERT Solutions for Class 7 Maths Chapter 7 Congruence of Triangles InText Questions<\/h2>\n

NCERT In-text Question Page No. 140 and 141<\/span>
\nQuestion 1.
\nLengths of the sides of the triangles are indicated. By applying the SSS congruence rule, state which pairs of triangles are congruent. In case of congruent triangles, write the result in symbolic form:
\n\"NCERT
\n\"NCERT
\nAnswer:
\n(i) In\u0394ABC and \u0394PQR such that
\nAB = 1.5 cm; PQ =1.5 cm
\n\u2234 AB = PQ
\nBC = 2.5 cm; QR = 2.5 cm
\n\u2234 BC = QR
\nAC = 2.2 cm and PR = 2.2 cm
\n\u2234 AC = PR
\n\u2234 The three sides of \u0394ABC are equal to the three sides of \u0394PQR.
\n\u2234 \u0394ABC \u2245 \u0394PQR
\n( By SSS congruence criterion)<\/p>\n

(ii) In \u0394DEF and \u0394LMN
\nDE = 3.2 cm, MN = 3.2
\n\u2234 DE = NM
\nEF = 3 cm; LM = 3 cm
\n\u2234 EF = LM
\nDF = 3.5 cm, LN = 3.5 cm
\n\u2234 DF = LN
\n\u2234 The three sides of \u0394DEF are equal to three sides of ALMN.
\n\u0394DEF \u2245 \u0394NML
\n(By SSS congruence criterion)<\/p>\n

(iii) In \u0394ABC and \u0394PQR,
\n\u2234 AC = 5 cm, PR = 5 cm
\n\u2234 AC = PR
\nBC = 4 cm, PQ = 4 cm
\n\u2234 BC = PQ
\nAB = 2 cm, QR = 2.5 cm
\nAB \u2260 QR
\nAB \u2260 QR
\n\u0394ABC and \u0394PQR are not congruent,<\/p>\n

(iv) We have \u0394ABD and \u0394ADC., such that
\nAB = 3.5 cm, AC = 3.5 cm
\n\u2234 AB = AC
\nBD = 2.5 cm, CD = 2.5 cm
\nAD is common ( AD = AD)
\nsince three sides of \u0394ABD are equal to the three sides of \u0394ACD
\n\u2234 The two triangles are congruent.
\n\u0394ABD \u2245 \u0394ACD
\n(SSS Congruence criterion)<\/p>\n

\"NCERT<\/p>\n

Question 2.
\nIn the given figure, AB = AC and D is the mid- point of \\(\\overline{\\mathrm{BC}}\\)
\n(i) State the three pairs of equal parts in \u0394ADB and \u0394ADC.
\n(ii) Is \u0394ADB \u2245 \u0394ADC? Give reasons.
\n(iii) Is \u2220B = \u2220C ? Why?
\n\"NCERT
\nAnswer:
\n(i) Here, AB = AC and D is the midpoint of \\(\\overline{\\mathrm{BC}}\\)
\n\u2234 BD = DC
\nIn \u0394ADB and \u0394ADC,
\nAB = AC, BD = DC
\nAD = AD (common)<\/p>\n

(ii) The three sides of \u0394ADB are equal to the three sides of \u0394ADC
\nBy SSS rule of congruence criterion
\n\u0394ADB \u2245 \u0394ADC<\/p>\n

(iii) Since \u0394ADB \u2245 \u0394ADC,
\n\u2220B = \u2220C (CPCT)<\/p>\n

Question 3.
\nIn the given figure, AC = BD and AD = BC. Which of the following statement is meaningfully written?
\n(i) \u0394ABC \u2245 \u0394ABD
\n(ii) \u0394ABC \u2245 \u0394BAD
\n\"NCERT
\nAnswer:
\nHave AC = BD and AD = BC
\nIn the given triangles ABC and ABD
\nAB = AB (common)
\nBD = AC (Given)
\nAD = BC (Given)
\nThree sides of \u0394ABD are equal to the three sides of \u0394ABC .So the two triangles are congruent,
\n\u2234 A \u2194 B; B \u2194 A; D \u2194 C
\n(i) \u0394ABC \u2245 \u0394ABD is not true or meaningless.
\n(ii) \u0394ABC \u2245 \u0394BAD is true or meaningful.<\/p>\n

\"NCERT<\/p>\n

NCERT In-text Question Page No. 143 & 144<\/span>
\nQuestion 1.
\nWhich angle is included between the sides \\(\\overline{\\mathrm{DE}}\\) and \\(\\overline{\\mathrm{EF}}\\) is \u0394DEF.
\nAnswer:
\nIn ADEF, the angle between \\(\\overline{\\mathrm{DE}}\\) and \\(\\overline{\\mathrm{EF}}\\), is \u2220DEF.<\/p>\n

Question 2.
\nBy applying SAS congruence rule, you want to establish that \u0394PQR \u2245 \u0394FED. It is given that PQ = FE and RP = DF. What additional information is needed to establish the congruence?
\nAnswer:
\nWe have \u0394PQR = \u0394FED
\n[Using SAS congruence rule]
\n\u2234 P \u2194 F, Q \u2194 E, R \u2194 D
\nand PQ = FE and RP = DF.
\n\"NCERT<\/p>\n

Question 3.
\nThe given measures of some parts of the triangles are indicated. By applying SAS congruence rule, state the pairs of congruence triangles, if any in each case. In case of congruent triangles, write them in symbolic form.
\n\"NCERT
\n\"NCERT
\nAnswer:
\n(i) \u0394ABC and \u0394DEF are congruent
\nAB = 2.5 cm; DE = 2.5 cm
\n\u2234 AB = DE
\nAC = 2.8 cm, DF = 2.8 cm
\n\u2234 AC = DF
\n\u2220A = 80\u00b0; \u2220D= 70\u00b0
\n\u2234 \u2220A \u2260\u2220D
\n\u2234 \u0394ABC and \u0394DEF are not congruent.<\/p>\n

(ii) In \u0394DEF and \u0394PQR
\nEF = 3 cm; QR = 3 cm
\n\u2234 EF = QR
\nFD = 3.5 cm; PQ = 3.5 cm
\n\u2234 FD = PQ
\n\u2220F = 40\u00b0, \u2220Q = 40\u00b0
\n\u2234 \u2220F = \u2220Q
\n\u2234 Two sides of \u0394ADE and their included angle are equal to the corresponding sides and their included angle of \u0394PQR
\n\u2234 The two triangles are congruent.
\n\u0394DEF \u2245 \u0394PQR
\n(SAS Congruence rule)<\/p>\n

(iii) In \u0394ABC and \u0394PQR.
\nAC = 2.5 cm, PR = 2.5 cm
\n\u2234 AC = PR
\nBC = 3 cm; PQ = 3 cm
\n\u2234 BC = PQ
\n\u2220C = 35\u00b0 = \u2220P = 35\u00b0
\n\u2234 \u2220C = \u2220P
\n\u2234 Two sides of \u0394ABC and their included angle are equal to the two corresponding sides and their included angle of \u0394PQR.
\n\u2234 \u0394ABC \u2245 \u0394RQP<\/p>\n

(iv) In the \u0394PRS and \u0394QPR
\nPQ = 3.5 cm, SR = 3.5 cm
\n\u2234 PQ = SR
\nPR = PR (PR is common)
\n\u2220QPR = 30\u00b0\u2220PRS = 30\u00b0
\n\u2234 Two sides of \u0394QPR and their included angle are equal to the corresponding sides and their included angle of \u0394PRS.
\n\u2234 \u0394PQR \u2245 \u0394RPS
\n(SAS congruence rule)<\/p>\n

\"NCERT<\/p>\n

Question 4.
\nIn the given Figure, \\(\\overline{\\mathrm{AB}}\\) and \\(\\overline{\\mathrm{CD}}\\) bisect each other at O.
\n(i) State the three pairs of equal parts in two triangles AOC and BOD.
\n(ii) Which of the following statements are true?
\n(a) \u0394AOC \u2245 \u0394DOB
\n(b) \u0394AOC \u2245 \u0394BOD
\n\"NCERT
\nAnswer:
\nSince \\(\\overline{\\mathrm{AB}}\\) and \\(\\overline{\\mathrm{CD}}\\) bisect each other at O.
\nAO = BO and CO = DO
\n\u2220AOC = \u2220BOD
\n(vertically opposite angles are equal)<\/p>\n

(i) In \u0394AOC and \u0394BOD
\nwe have, AO = BO and CO = DO
\n\u2220AOC = \u2220BOD<\/p>\n

(ii) From the above given relation
\n\u0394AOC \u2245 \u0394BOD
\n(By SAS congruence rule)
\n(a) The statement \u0394AOC \u2245 \u0394DOB is false.
\n(b) The statement \u0394AOC \u2245 \u0394BOD is true.<\/p>\n

NCERT In-text Question Page No. 145 & 146<\/span>
\nQuestion 1.
\nWhat is the side included between the angles M and N of \u0394MNP?
\nAnswer:
\nIn AMNP, the side included between M and N is \\(\\overline{\\mathrm{MN}}\\).<\/p>\n

Question 2.
\nYou want to establish \u0394DEF \u2245 \u0394MNP, using the ASA congruence rule. You are given that \u2220D = \u2220M and \u2220F = \u2220P. What information is needed to establish the congruence? (Draw a rough figure and then try!)
\nAnswer:
\nTo establish \u0394DEF \u2245 \u0394MNP, using ASA congruence rule, we need the side containing \u2220D and \u2220F to be equal to the side containing \u2220M and \u2220P.
\n\"NCERT
\ni. e. We need \\(\\overline{\\mathrm{DF}}=\\overline{\\mathrm{MP}}\\).<\/p>\n

Question 3.
\nIn the given figure, PL\u22a5OB and PM\u22a5OA such that PL = PM. Prove that \u0394PLO \u2245 \u0394PMO
\n\"NCERT
\nAnswer:
\nIn \u0394PLO and \u0394PMO, we have
\n\u2220PLO = \u2220PMO = 90\u00b0
\n(Given)
\nOP = OP (Hypotenuse – common side)
\nPL = PM (Given)
\nBy using RHS Congruency, we get
\n\u0394PLO \u2245 \u0394PMO<\/p>\n

\"NCERT<\/p>\n

Question 4.
\nGiven below are measurements of some parts of two triangles. Examine whether the two triangles are congruent or not, by ASA congruence rule. In case of congruence, write it in symbolic form.
\n\u0394DEF
\n(i) \u2220D = 60\u00b0, \u2220F = 80\u00b0, \u2220DF = 5 cm
\n(ii) \u2220D = 60\u00b0, \u2220F = 80\u00b0, DF = 6cm
\n(iii) \u2220E = 80\u00b0, \u2220F = 30\u00b0, EF = 5 cm<\/p>\n

\u0394PQR
\n(i) \u2220Q = 60\u00b0, \u2220R = 80\u00b0, QR = 5cm
\n(ii) \u2220Q = 60\u00b0, \u2220R = 80\u00b0, QP = 6cm
\n(iii) \u2220P = 80\u00b0, PQ = 5 cm, \u2220R = 30\u00b0
\nAnswer:
\n(i) Since \u2220D = \u2220Q (each = 60\u00b0)
\n\u2220F = \u2220R (each = 80\u00b0)
\nIncluded side DF = Included side QR [each = 5 cm]
\n\u2234 Using ASA congruence rule, we can say that two triangles are congruent.
\nAlso, D \u2194 Q, F \u2194 R and E \u2194 P
\n\u2234 \u0394DEF \u2245 \u0394QPR<\/p>\n

(ii) Here, QP is not the included side.
\n\u2234 The given triangles are not congruent.<\/p>\n

(iii) Here, PQ is not the included side.
\n\u2234 The given triangles are not congruent.<\/p>\n

Question 5.
\nIn the given figure ray AZ bisects \u2220DAB as well as \u2220DCB.
\n(i) State the three pairs of equal parts in triangles BAC and DAC.
\n(ii) Is \u0394BAC \u2245 \u0394DAC? Give reasons.
\n(iii) Is AB = AD? justify your answer.
\n(iv) Is CD = CB? Give reasons.
\n\"NCERT
\nAnswer:
\n(i) AC is the bisector of \u2220DAB as well as of \u2220DCB
\n\u2234 \u2220DAC = \u2220BAC and \u2220DCA = \u2220BCA
\nIn \u0394BCA and \u0394DAC equal parts are
\nAC = AC (Common)
\n\u2220DAC = \u2220BAC (AC is a bisector)
\n\u2220DCA = \u2220BCA (AC is a bisector)<\/p>\n

(ii) From the above relation, the two triangles are congruent (using ASA congruence rule)
\nA \u2194 A C \u2194 C and D \u2194 B
\n\u2234 \u0394ADC \u2245 \u0394ABC
\nor
\n\u0394BAC \u2245 \u0394DAC<\/p>\n

(iii) Since \u0394BAC \u2245 \u0394DAC The corresponding parts are equal.
\n\u2234 AB = AD<\/p>\n

(iv) Since \u0394BAC \u2245 \u0394DAC
\n\u2234 CD = CB (Corresponding parts are equal)<\/p>\n

\"NCERT<\/p>\n

NCERT In-text Question Page No. 148 <\/span>
\nQuestion 1.
\nIn the given figure measures of some parts of triangles are given. By applying R.H.S congruence rule, state which pairs of triangles are congruent. In case of congruent triangles, write the result in symbolic form.
\n\"NCERT
\n\"NCERT
\nAnswer:
\n(i) In the right \u0394PQR and right \u0394DEF Hypotenuse PR = Hypotenuse DF (each 6 cm)
\nPQ = 3 cm, DE = 2.5 cm
\nPQ \u2260 DE
\n\u2234 \u0394PQR is not congruent to \u0394DEF<\/p>\n

(ii) Right \u0394ABC and right \u0394ABD we have two right triangles ABC and ABD such that
\nHypotenuse AB = Hypotenuse BA (common)
\nAC = 2 cm, BD = 2 cm
\n\u2234 AC = BD \u2220C = \u2220D = 90\u00b0
\nBuy using RHS congruence rule, we can say that the two right triangles are congruent
\n\u2234 \u0394ABC \u2245 \u0394BAD<\/p>\n

(iii) Right \u0394ABC and Right \u0394ACD, We have right \u0394ABC and right \u0394ACD such that Hypotenuse AC = Hypotenuse AC (common) side \\(\\overline{\\mathrm{AB}}\\) = side \\(\\overline{\\mathrm{AD}}\\) (each 3.6 cm)
\n\u2234 The two right triangles are congruent.
\n\u2234 \u0394ABC \u2245 \u0394ADC<\/p>\n

(iv) Right \u0394PQS and Right \u0394PRS
\nHypotenuse PQ = Hypotenuse PR (each 3 cm)
\nside PS = side PS (common)
\n\u2234 using R.H.S congruence rule that two right triangles are congruent.
\n\u2234 i.e., \u0394PQS \u2245 \u0394PRS<\/p>\n

Question 2.
\nIt is to be established by RHS congruence rule that \u0394ABC \u2245 \u0394RPQ. What additional information is needed, if it is given that \u2220B = \u2220P = 90\u00b0 and AB = RP?
\nAnswer:
\nWe have \u0394ABC \u2245 \u0394RPQ
\nSince, \u2220B = 90\u00b0 \u21d2 Side AC is hypotenuse and \u2220P = 90\u00b0 \u2245 Side RQ is hypotenuse.
\nThe required information needed is Hypotenuse
\nAC = Hypotenuse RQ.<\/p>\n

\"NCERT<\/p>\n

Question 3.
\nIn the given figure, BD and CE are altitudes of \u0394ABC such that BD = CE.
\n(i) State the three pairs of equal parts in \u0394CBD and \u0394BCE.
\n(ii) Is \u0394CBD \u2245 \u0394BCE? why or why not?
\n(iii) Is \u2220DCB = \u2220EBC? why or why not?
\n\"NCERT
\nAnswer:
\n(i) Hypotenuse BC = Hypotenuse BC
\n(common)
\nside BD = side CE (Given)
\n\u2220BEC = \u2220BDC= 90\u00b0
\nThe above are the three equal parts in \u0394CBD and \u0394BCE<\/p>\n

(ii) \u2220D = \u2220E and \u2220B = \u2220C
\n\u2234 \u0394CBD \u2245 \u0394BCE (By RHS)<\/p>\n

(iii) Since \u0394CBD \u2245 \u0394BCE
\n\u2220DCB =\u2220EBC
\n( \u2235 their corresponding parts are equal)<\/p>\n

Question 4.
\nABC is an isosceles triangle with AB = AC and AD is one of its altitudes.
\n(i) State the three pairs of equal parts in \u0394ADB and \u0394ADC.
\n(ii) Is \u0394ADB \u2245 \u0394ADC? why or why not?
\n(iii) Is \u2220B = \u2220C? why or why not?
\n(iv) Is BD = CD? why or why not?
\n\"NCERT
\nAnswer:
\n(i) The three pairs of equal parts in \u0394ADB and \u0394ADC are
\nAD = AD (common)
\nHypotenuse AB = Hypotenuse AC
\n(Given)
\n\u2220ADB = \u2220ADC (each 90\u00b0)<\/p>\n

(ii) A \u2194 A, B \u2194 C, D \u2194 D
\n\u2234 \u0394ADB \u2245 \u0394ADC (RHS)<\/p>\n

(iii) \u0394ADB \u2245 \u0394ADC
\nAs, corresponding parts are equal.
\n\u2234 \u2220B = \u2220C<\/p>\n

(iv) \u0394ADB \u2245 \u0394ADC
\nAs corresponding parts are equal.
\nBD = CD<\/p>\n","protected":false},"excerpt":{"rendered":"

These NCERT Solutions for Class 7 Maths Chapter 7 Congruence of Triangles InText Questions and Answers are prepared by our highly skilled subject experts. NCERT Solutions for Class 7 Maths Chapter 7 Congruence of Triangles InText Questions NCERT In-text Question Page No. 140 and 141 Question 1. Lengths of the sides of the triangles are …<\/p>\n

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