If `D` is the mid-point of the hypotenuse `A C` of a right triangle `A B C ,` prove that `B D=1/2A C`

Explanation

To prove that \( BD = \frac{1}{2} AC \) in triangle \( ABC \) where \( D \) is the midpoint of the hypotenuse \( AC \), we will follow the steps outlined below:

### Step-by-Step Solution:

1. **Construct the Triangle and Extend BD:**
- We have triangle \( ABC \) with \( D \) as the midpoint of hypotenuse \( AC \).
- Extend line segment \( BD \) to point \( E \) such that \( BD = DE \).

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