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?

Answer:

\(\overline{\mathrm{PM}}\) is an altitude of ΔPQR.

\(\overline{\mathrm{PD}}\) is a median of ΔPQR.

QM ≠ MR

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.

(b) In the right ΔQPR, \(\overline{\mathrm{PQ}}\) and \(\overline{\mathrm{PR}}\) are altitudes of the triangle.

(c) In the figure, \(\overline{\mathrm{YL}}\) is an altitude of ΔXYZ.

Question 3.

Verify by drawing a diagram if the median and altitude of an isosceles triangle can be same.

Answer:

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.