If the altitude from one vertex of a triangle bisects the opposite side, then the triangle is isosceles. GIVEN : A `A B C` such that the altitude `A D` from `A` on the opposite side `B C` bisects `B C` i.e., `B D=D Cdot` TO PROVE : `A B=A C` i.e. the triangle `A B C` is isosceles.

Explanation

To prove that triangle ABC is isosceles given that the altitude AD from vertex A bisects the opposite side BC, we will follow these steps:

### Step-by-Step Solution:

1. **Given Information**: We have triangle ABC with altitude AD from vertex A to side BC. It is given that AD bisects BC, meaning BD = DC.

2. **Identify Triangles**: We will consider triangles ABD and ADC.

...