Gujarat Board GSEB Textbook Solutions Class 7 Maths Chapter 6 The Triangles and Its Properties Ex 6.1 Textbook Questions and Answers.

## Gujarat Board Textbook Solutions Class 7 Maths Chapter 6 The Triangles and Its Properties Ex 6.1

Question 1.

In ∆PQR, D is the mid-point of \(\overline{Q R}\).

\(\overline{P M}\) is _______

PD is _______

Is QM = MR?

Solution:

PM is an altitude of ∆PQR.

PD is a median of ∆PQR.

No, QM ≠ MR.

Question 2.

Draw rough sketches for the following:

(a) In ∆ABC, BE is a median.

(b) In ∆PQR, PQ and PR are altitudes of the triangle.

(c) In ∆XYZ, YL is an altitude in the exterior of the triangle.

Solution:

(a) In the adjoining figure, \(\overline{B E}\) is a median of AABC.

(b) In right ∆QPR, \(\overline{P Q}\) and \(\overline{P R}\) are altitudes of the triangle.

(c) In the following figure, \(\overline{Y L}\) is an altitude of ∆XYZ.

Question 3.

Verify by drawing a diagram if the median and altitude of an isosceles triangle can be same. Solution: In the adjoining figure, ∆ABC is an isosceles triangle having AB = AC.

Draw its median AD. Now, with the help of a protractor, measure the ∠ADB.

We find that

∠ADB = 90°

∴ AD is a perpendicular to BC

Thus, \(\overline{A D}\) is the median as well as an altitude of ∆ABC.