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 the quadrilateral PQRS is a rhombus, we will follow these steps:

### Step 1: Identify the midpoints
Let P, Q, R, and S be the midpoints of sides AB, BC, CD, and DA of quadrilateral ABCD respectively.

### Step 2: Apply the Midpoint Theorem in triangles
1. In triangle ADC:
- S is the midpoint of AD and R is the midpoint of CD.
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