NCERT Solutions for Class 7 Maths Chapter 6 The Triangles and Its Properties Ex 6.1

These NCERT Solutions for Class 7 Maths Chapter 6 The Triangles and Its Properties Ex 6.1 Questions and Answers are prepared by our highly skilled subject experts.

NCERT Solutions for Class 7 Maths Chapter 6 The Triangles and Its Properties Exercise 6.1

Question 1.
In ΔPQR, D is the mid-point of \(\overline{\text { QR }}\).
PM is ……………
PD is ……………
Is QM = MR?
NCERT Solutions for Class 7 Maths Chapter 6 The Triangles and Its Properties Ex 6.1 1
Answer:
\(\overline{\mathrm{PM}}\) is an altitude of ΔPQR.
\(\overline{\mathrm{PD}}\) is a median of ΔPQR.
QM ≠ MR

NCERT Solutions for Class 7 Maths Chapter 6 The Triangles and Its Properties Ex 6.1

Question 2.
Draw rough sketches for the following:
(a) In ΔABC, BE is a median.
(b) In ΔPQR, PQ and PR are altitudes of the triangle.
(c) In ΔXYZ, YL is an altitude in the exterior of the triangle.
Answer:
(a) In the ΔABC, \(\overline{\mathrm{BE}}\) is the median.
NCERT Solutions for Class 7 Maths Chapter 6 The Triangles and Its Properties Ex 6.1 2

(b) In the right ΔQPR, \(\overline{\mathrm{PQ}}\) and \(\overline{\mathrm{PR}}\) are altitudes of the triangle.
NCERT Solutions for Class 7 Maths Chapter 6 The Triangles and Its Properties Ex 6.1 3

(c) In the figure, \(\overline{\mathrm{YL}}\) is an altitude of ΔXYZ.
NCERT Solutions for Class 7 Maths Chapter 6 The Triangles and Its Properties Ex 6.1 4

NCERT Solutions for Class 7 Maths Chapter 6 The Triangles and Its Properties Ex 6.1

Question 3.
Verify by drawing a diagram if the median and altitude of an isosceles triangle can be same.
Answer:
NCERT Solutions for Class 7 Maths Chapter 6 The Triangles and Its Properties Ex 6.1 5
ABC is an isosceles triangle having
AB = AC …(i)
Draw its median AD.
Consider ΔADB and ΔADC
AB = AC (By (i))
AD = AD (Common)
BD = DC
(Since AD is median)
⇒ ΔADB = ΔADC (SSS)
⇒ ∠ADB = ∠ADC = 90°
(Corresponding angles)
∠ADB = 90°
∵ \(\overline{\mathrm{AD}}\) is a perpendicular to \(\overline{\mathrm{BC}}\).
Thus, \(\overline{\mathrm{AD}}\) is the median as well as the altitude of ΔABC.

error: Content is protected !!