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.,
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)
hence, PQRS is a rhombus.. .