In the given figure, if PQ || RS, prove that ΔPOQ ~ Δ SOR. – InterviewSolution

InterviewSolution

1.

In the given figure, if PQ || RS, prove that ΔPOQ ~ Δ SOR.

Answer»

Given: PQ || RS

To Prove: ΔPOQ ~ ΔSOR

Let us take ΔPOQ and ΔSOR

∠OPQ = ∠OSR (as PQ || RS, Alternate angles)

∠POQ = ∠ROS (vertically opposite angles)

∠OQP = ∠ORS (as PQ || RS, Alternate angles)

∴ ΔPOQ ~ ΔSOR (by AAA similarity criterion)

Hence Proved

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