Question

PQRS is an isosceles trapezium where PQ||SR and PS=QR. PS and QR are extended to meet at O. Prove SO=RO.​

Answer 1

In Δ SOR ,

PQ||SR. (given)

Therefore by basic proportionality theorem

SO/PS = RO\QR

But PS = QR. (given)

Therefore SO = RO.

Answer 2

op/ps= oq/qr,( w.k.t.)pq|| sr

opq^ = osr^{ corresponding angles)

anhle opq = amgle ors

so, ops = oqr ( by above solving)

so,so = ro hence proved