PQRS is a trapezium with PQ SR. Diagonals PR and SQ intersect at M. Δ

1.	PQRS is a trapezium with PQ SR. Diagonals PR and SQ intersect at M. ΔΡ MS-aQMR. Prove thatPS QR
Answer» Given ΔPMS andΔQMR are similar. So the ratios of corresponding sides are: PM/ MR = QM / MS = PS/ QR We have thatAr(ΔPSR) = Ar(ΔQSR) , as the altitude and base are equal. Hence Ar(ΔPMS+ΔMSR) = Ar(ΔQMR +ΔMSR)Hence Ar(ΔPMS ) = Ar(ΔQMR) The ratio ofareas of similar triangles = square of ratio of corresponding sides. If the areas of similar triangles are equal, it means the correspondingsides are equal. Hence, PS = QR

PQRS is a trapezium with PQ SR. Diagonals PR and SQ intersect at M. ΔΡ MS-aQMR. Prove thatPS QR

Answer»

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

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

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

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

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

Hence, PS = QR