InterviewSolution
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InterviewSolution
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Given: In trapezium PQRS, side PQ || side SR, AR = 5 AP, AS = 5 AQ, then prove that SR = 5 PQ |
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Answer» side PQ || side SR [Given] and seg SQ is their transversal. ∴ ∠QSR = ∠SQP [Altemate angles] ∴ ∠ASR = ∠AQP (i) [Q – A – S] In ∆ASR and ∆AQP, ∠ASR = ∠AQP [From (i)] ∠SAR ≅ ∠QAP [Vertically opposite angles] ∆ASR ~ ∆AQP [AA test of similarity] ∴ AS/AQ = SR/PQ (ii) [Corresponding sides of similar trianges] But, AS = 5 AQ [Given] ∴ AS/AQ = 5/1 (iii) ∴ SR/PQ = 5/1 [Form (ii) and (iii)] ∴ SR =5 PQ |
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