Question

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

Answer 1

Answer:

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,

Thinking Process

Firstly, use the mid-point theorem in various triangles of a quadrilateral. Further show that the line segments formed by joining the mid-points are equal, which prove the required quadrilateral.