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.