**AD is an altitude of an isosceles triangle ABC in which AB = AC. Show that**

**(i) AD bisects BC (ii) AD bisects ∠ A.**

**Solution (i)**

It is given that is isosceles with AB=AC and AD is perpendicular to BC.

We need to prove that BD=CD.

In and , we have

**(Given)**

**(Each given equal to )**

** (Common)**

Therefore, by RHS congruence rule,

Hence, we have BD=CD ** (Corresponding parts of congruent triangles are equal).**

**Solution (ii)**

We have proved above that .

It means that ** (Corresponding parts of congruent triangles are equal).**

means that AD bisects .