The diagonals of a quadrilateral `A B C D` are perpendicular. Show that the quadrilateral, formed by joining the mid-points of its sides, is a rectangle.

Explanation

To show that the quadrilateral formed by joining the midpoints of the sides of quadrilateral ABCD, where the diagonals are perpendicular, is a rectangle, we can follow these steps:

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

### Step 2: Use the Midpoint Theorem
According to the Midpoint Theorem, the line segment joining the midpoints of two sides of a triangle is parallel to the third side and half its length.

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