Question

PQRS is a trapezium with pq parallel to sr. diagonals pr and sq intersect at m.triangle pms and triangle qmr.prove that ps=qr.

Answer 1

See the diagram.   

Given ΔPMS  and  ΔQMR  are similar.  So the ratios of corresponding sides are:
       PM / MR = QM / MS = PS / QR

We have that Ar(ΔPSR) = Ar(ΔQSR) , as the altitude and base are equal.

Hence    Ar(ΔPMS+ΔMSR) = Ar(ΔQMR + ΔMSR) 
Hence     Ar(ΔPMS ) = Ar(ΔQMR)

The ratio of areas of similar triangles = square of ratio of corresponding sides.

If the areas of similar triangles are equal, it means the corresponding sides are equal.

Hence,  PS = QR

Answer 2

Answer:

think about it may

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