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In quadrilateral ABCD, the mid-points P, Q, R, S of the sides are joined in order to form a parallelogram PQRS. It is observed that PQRS turns out to be a rectangle.
What special property must the diagonals AC and BD of ABCD have?

Class 9The Mid-point TheoremGeometry — Quadrilaterals
  • Athey are perpendicular
  • Bthey are equal
  • Cthey bisect each other
  • Dthey are parallel

Step-by-Step Solution

Sides of PQRS are parallel to the diagonals AC and BD. For PQRS to have right angles (a rectangle), the diagonals AC and BD must be perpendicular.
Answer: A) they are perpendicular

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