**The Triangle and its Properties**

**Question 1.**

**Solution:**

**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)** Rough sketch of median BE of ∆ABC is as shown.**(b)** Rough sketch of altitudes PQ and PR of ∆PQR is as shown.**(c)** Rough sketch of an exterior altitude YL of ∆XYZ is as shown.

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

**Solution:**

Draw a line segment BC. By paper folding, locate the perpendicular bisector of BC. The folded crease meets BC at D, its mid-point.

Take any point A on this perpendicular bisector. Join AB and AC. The triangle thus obtained is an isosceles ∆ABC in which AB = AC.

Since, D is the mid-point of BC, so AD is its median. Also AD is the perpendicular bisector of BC. So, AD is the altitude of ∆ABC.

Thus, it is verified that the median and altitude of an isosceles triangle are same.