Question

in the figure pqrs is a trapezium in which pqllrs and ps=qr.show that triangle pqr is congruent to triangle qps and pr=qs

Answer 1

In PQR and QPS,
<P=<Q(prop. of isotrap.)
PQ=PQ(common)
PS=QR(given)
Therefore, PQR is congruent to QPS.
PR=QS(C.P.C.T)
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Answer 2

in triangle qps and triangle pqr

ps = qr (given)

pq = pq (given)

<spq = <rqp (property of iso. trapezium)

therefore, triangle qps = triangle pqr (by S.A.S. axiom)

also, pr = qs (by C.P.C.T.)

----------------Hence, Proved.----------------------------