Question

what is the answer for this question

Answer 1

Hello Mate!

Given : ar(∆POQ) = ar(∆ROS)

To prove : PQRS is trapezium

Proof : ar(∆POQ) = ar(∆ROS) [ Given ]

Adding ar(∆POS) both sides we get,

ar(∆POQ) + ar(∆POS) = ar(∆ROS) + ar(∆POS)

ar(∆QPS) = ar(∆PSR)

Hence ∆QPS and ∆PSR are such two triangles that lie on same base PS and have same area so they must lie between same parallels too.

Therefore, PS || QR and hence PQRS is a trapezium since its one pair of opposite sides are parallel.

Hence proved.

Have great future ahead!