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In figure, if PQ||RS, prove that DeltaP...

In figure, if PQ||RS, prove that `DeltaP O Q DeltaS O R`.

Text Solution

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Given: `PQ || RS`
To Prove: `trianglePOQ ~ triangleSOR`
Let us take `trianglePOQ` and `triangleSOR`
`/_OPQ = /_OSR` (as `PQ || RS,` Alternate angles)
`/_POQ = /_ROS` (vertically opposite angles)
`/_OQP = /_ORS` (as `PQ || RS`, Alternate angles)
`trianglePOQ ~ triangleSOR` (by AAA similarity criterion) Hence Prove
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