the diagonal PR of a parallelogram PQRS bisect the angle R . prove thatPQRS is a rhombus.

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GIVEN: - A parallelogram PQRS whose daigonals PR and QS intersect each other at O. such that PR perpendicular To QS..

To prve:- PQRS is a rhombus

Proof: - since the daigonal of parallelogram bisect each other .,   we have : OP= OR and OQ= OS.

Now, in triangle POS and ROS, we have., 

OP=OR

angle POS= angle ROS= 90

and OS is comman

then.. triangle POS congruent to triangle ROS

:. PS= RS (c.p.c.t)

Now, PQ= RS and PS= RQ (opposite side of parallelogram)

and PS=RS (proved)

:. PQ=QR=RS=SP..

hence, PQRS is a rhombus.. .

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