Question

PQRS is a trapezium PQ parallel SR . SR is produced to X so that RX=PQ. Prove that arc ∆PSQ = ar ∆QRX

Answer 1

I hope this clears your doubt!

Answer 2

Proved below.

Step-by-step explanation:

Given: PQRS is trapezium with PQ // SR, RX = PQ

To prove: ar (∆ PSQ)= ar (∆ QRX)

Proof:

PQ // SR (given)

:. ar (∆ PSQ) = ar (∆ PQR)              [1] (parallelorams on the same base PQ and between same parallels)

In triangles PQR and XRQ  

PO = XR                (GIVEN)

QR=QR(common)

angle Q =angle R  (PQ // SR alternate interior angles)

:. triangle PQR congruent to triangle XRQ (SAS)

:. ar (∆ PQR) = ar (∆ QRX)                [2]   (congruent figures are equal in area)

From equqtipn 1 and 2

ar (∆ PSQ) = ar (∆ PQR)= ar(∆ QRX)

Hence ar (PSQ) = ar (QRX)

Hence proved.