Question

ABCD is a rhombus and P,Q,R,S are mid-points of AB, BC,CD and DA respectively. Prove that quadrilateral PQRS is a rectangle.

In the middle of the city, there was a park ABCD in the form of a parallelogram form so that AB = CD, AB||CD and AD = BC, AD||BC. Municipality converted this park into a rectangular form by adding land in the form of △APD and △BCQ. Both the triangular shape of land were covered by planting flower plants.