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Question
In given fig., quadrilateral PQRS, side PQ || side SR, AR = 5 AP, then prove that, SR = 5PQ
Solution
side PQ || side SR and seg SQ is their transversal. ...[Given]
∴ ∠QSR ≅ ∠SQP ...[Alternative angles]
∴ ∠ASR ≅ ∠AQP ......(i) [Q−A−S]
In ΔASR and ΔAQP,
∠ASR ≅ ∠AQP ......[From (i)]
∠SAR ≅ ∠QAP ......[Vertically opposite angles]
∴ ΔASR ∼ ΔAQP ......[AA test of similarity]
∴ `"AR"/"AP" = "SR"/"PQ"` ......(ii)[Corresponding sides of similar triangles]
But, AR = 5 AP ......[Given]
∴ `"AR"/"AP" = 5/1` ......(iii)
∴ `"SR"/"PQ" = 5/1` ......[From (ii) and (iii)]
∴ SR = 5PQ
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