Question

complete the statement.
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Answer 1

Answer:

Given:

side PQ || side SR

AR = 5AP,

AS = 5AQ

To prove: SR = 5PQ

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

Corresponding sides are proportional

PQSR=APAR( Corresponding sides are proportional )

⇒PQSR=15(AR=5AP)

⇒SR=5PQ

Hence proved.