A kite has congruent adjacent sides so that and

MATHEMATICS · Subjective · CBSE · Mathematics · Triangles · Triangles

Problem

A kite

PQRS

has congruent adjacent sides so that

PQ = PR

and

SQ = SR

. Its diagonals

PR

and

QS

intersect at

O

. (a) Prove that

\triangle PQO \cong \triangle PRO

. (b) Prove that

\triangle SQO \cong \triangle SRO

. (c) Using the above, establish that

\angle POQ = \angle ROS

and conclude that the diagonals of the kite are perpendicular. Present your reasoning in a logical chain of congruences.