Question

P,Q,R,S are respectively the mid-points of sides AB,BC,CD,DA of quadrilateral ABCD such that AC perpendicular BD.Prove that PQRS is a rectangle.

Answer 1

if AC is perpendicular to BD the quadrilateral ABCD is likely to be a rhombus and if we join the midpoints of all the sides of a rhombus the resulting quadrilateral with always be a rectangle as the opposite sides will be equal