Given : In trapezium PQRS, side PQ || side SR, AR = 5AP, AS = 5AQ then prove that, SR = 5PQ

Given side PQ side SR.
Also AR = 5AP, AS = 5AQ
SQ is the transversal of parallel sides PQ and SR.
QSR = PQS [ Alternate interior angles]
ASR = AQP….(i) [ Alternate interior angles]
Consider ASR and AQP
ASR = AQP From (i)
SAR = QAP [ vertical opposite angles]
ASR ~ AQP [ AA test of similarity]
AS/AQ = SR/PQ [ Corresponding sides of similar triangles]
AS = 5AQ [Given]
AS/AQ = 5/1
SR/PQ = 5/1
SR = 5PQ
Hence proved.