Question

In given fig., quadrilateral PQRS, side PQ || side SR, AR = 5 AP, then prove that, SR = 5PQ

Answer 1

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