Question

in trapezium pQRS ,side pQ||sideSR ,AR=5AP,AS=5PQ,then prove that SR=5PQ​

Answer 1

Answer:

Trapezium

Step-by-step explanation:

Given:

Side PQ || Side SR

AR = 5 AP

AR = 5 PQ

To prove:

SR = 5 PQ

Proof:

In △APQ and △ARS

∠PAQ = ∠RAS (Vertically Opposite Angles)

∠PQA = ∠RSA. (Alternate Angles, side PQ || side SR and QS is a transversal line)

By AA test of similarity

△APQ ~ △ARS

$\frac{pq}{sr} = \frac{ap}{ar}$

(Corresponding sides are)

$\frac{pq}{sr} = \frac{1}{5} (ar = 5ap)$

——> SR = 5 PQ

Hence proved