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` . GIVEN : A `A B C` in which `/_B=90^0` and `D` is the mid-point of `A Cdot` TO PROVE : `B D=1/2A C` CONSTRUCTION Produce `B D` to `E` so that `B D=D Edot` Join `E Cdot`

Explanation

To prove that \( BD = \frac{1}{2} AC \) given that \( D \) is the midpoint of the hypotenuse \( AC \) in right triangle \( ABC \) where \( \angle B = 90^\circ \), we can follow these steps:

### Step-by-Step Solution

1. **Given Information**: We have triangle \( ABC \) with \( \angle B = 90^\circ \) and \( D \) is the midpoint of hypotenuse \( AC \).

2. **Construction**: Extend \( BD \) to point \( E \) such that \( BD = DE \). Join \( EC \).

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