P, Q , R and S are respectively the mid-points of the sides AB, BC, CD and DA of a quadrilateral ABCD in which AC = BD. Prove that PQRS is a rhombus.

Explanation

To prove that quadrilateral PQRS is a rhombus, we need to show that its opposite sides are equal in length and that its diagonals bisect each other at right angles. Given that P, Q, R, and S are the midpoints of sides AB, BC, CD, and DA of quadrilateral ABCD, and that AC = BD, we can follow these steps:

### Step-by-Step Solution:

1. **Identify Midpoints**:
Let P, Q, R, and S be the midpoints of sides AB, BC, CD, and DA respectively.

2. **Use the Midpoint Theorem**:
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