Question

The diagonals of a quadrilateral are perpendicular to each other. The midpoints of its sides are joined to form another quadrilateral. Then, this quadrilateral is a square.

• A. False
• B. True

Answer 1

The correct option is A

False

Given : ABCD is a quadrilateral having AC perpendicular to BD P, Q, R, S are midpoint of its sides.

The line joining the midpoint of 2 sides of a triangle is parallel to 3rd side

PQ || BD

$\therefore$ $\angle Q={90}^{\circ }$ ( parallel lines property )

Similarly $\angle P=\angle Q=\angle R=\angle S={90}^{\circ };$ PQRS is a rectangle.