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Question
In trapezium PQRS, side PQ || side SR, AR = 5AP, AS = 5AQ then prove that, SR = 5PQ
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Solution
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
\[ \Rightarrow \frac{PQ}{SR} = \frac{1}{5} \left( AR = 5AP \right)\]
\[ \Rightarrow SR = 5PQ\]
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