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In trapezium PQRS, side PQ|| side SR, AR...

In trapezium `PQRS`, side `PQ||` side `SR`, `AR=5AP`, `AS=5AQ` then prove that `SR=5PQ` by completing the following activity.

In `DeltaPQA` and `DeltaRSA`,
`/_PQA~=/_RSA`……(`square`)
`/_PAQ~=/_RAS`....(`square`)
`:.DeltaPQA~DeltaRSA` ......(`square`)
`(PQ)/(SR)=(square)/(AR)`.........(Corresponding sides of similar triangles).....`(1)`
Substituting `AR=5AP` in `(1)`
`:.(PQ)/(SR)=(square)/(5AP)`
`:.(PQ)/(SR)=(square)/(5)`
`:.SR=5PQ`

Text Solution

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In `DeltaPQA` and `DeltaRSA`,
`/_PQA~=/_RSA`……(Alternate angle)
`/_PAQ~=/_RAS`....(Vertically opposite angles)
`:.DeltaPQA~DeltaRSA` ......("AA" test of similarity)
`(PQ)/(SR)=(AP)/(AR)`.........(Corresponding sides of similar triangles).....`(1)`
Substituting `AR=5AP` in `(1)`
`:.(PQ)/(SR)=(AP)/(5AP)`
`:.(PQ)/(SR)=(1)/(5)`
`:.SR=5PQ`
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