ABCD is a square. P, Q, R, S are the mid-points of AB, BC, CD and DA respectively. By joining AR, BS, CP, DQ, we get a quadrilateral which is a -Maths 9th
According to the given statement, the figure will be a shown alongside; using mid-point theorem: In △ABC,PQ∥AC and PQ=21AC .......(1) In △ADC,SR∥AC and SR=21AC .......(2) ∴PQ=SR and PQ∥SR from (1) and (2) ⇒PQRS is a parallelogram. Now,PQRS will be a rectangle if any angle of the parallelogram PQRS is 90∘ PQ∥AC(by midpoint theorem) QR=BD(by midpoint theorem) But AC⊥BD(diagonals of a rhombus are perpendicular to each other) ∴PQ⊥QR(angle between two lines = angle between their parallels) Hence PQRS is a rectangle.