**The Triangle and Its Properties ****Exercise 6.1 ****NCERT Solution for Class 7 Maths Chapter 6 **

**The Triangle and Its Properties ****Exercise 6.2**

**The Triangle and Its Properties ****Exercise 6.3**

**The Triangle and Its Properties ****Exercise 6.4**

**The Triangle and Its Properties ****Exercise 6.5**

**Exercise 6.1**

**Question 1. In ∆PQR, D is the mid-point of QR ,**

**PM is ____________**

**PD is _____________ **

** **

**Is QM = MR? **** **

**Solution 1:- **

Given, QD = DR and D is the mid point of QR

So, PM is altitude.

PD is median.

No, QM ≠ MR because D is the mid point of QR.

**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 2:-**

(a) BE is median in **∆ABC **and AE = EC

(b) PQ and PR are the altitudes of the triangle PQR and RP perpendicular to QP.

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

**Question 3 :- Verify by drawing a diagram if the median and altitude of an isosceles triangle can be same.**

**Solution 3:-**

∆ABC is an isosceles triangle in which AB = AC

Draw AL, as the median of the triangle.

Measure the angle ALC with the help of protractor

we find, ∠ALC = 90°

Thus, AL is the median as well as the altitude of the ∆ABC.

Hence Verified.

**NCERT Solutions for Class 7 Math, Chapter 6 – The Triangle and Its Properties, ****Exercise-6.1**