`A B C` is a triangle and `D` is the mid-point of `B C` . The perpendiculars from `D` to `A B` and `A C` are equal. Prove that the triangle is isosceles.

Explanation

To prove that triangle ABC is isosceles given that D is the midpoint of BC and the perpendiculars from D to AB and AC are equal, we can follow these steps:

### Step 1: Identify Given Information
We are given:
- Triangle ABC
- D is the midpoint of BC, so \( BD = CD \)
- The perpendiculars from D to AB and AC are equal, so \( DE = DF \)

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