Question

ABC is a triangle and D is the mid-point of BC. The perpendiculars from D to AB and AC are equal. Prove that the triangle is-isosceles.

Answer 1

We have to prove thatis isosceles.

Let and be perpendicular from D on AB and AC respectively.

In order to prove that

We will prove that

Now in and we have

(Since D is mid point of BC)

(Given)

So by congruence criterion we have

And

Hence is isosceles.