Question

In trapezium PQRS, $SidePQ||sideSR$ $AR=5AP$ $AS-5AQ$, then prove that $SR=5PQ$

Answer 1

REF.Image

PQ||RS

$\angle QPA=\angle ASR$

$\angle QRA=\angle ARS$

$\angle PAQ=\angle SAR$

AAA similarity Theorem

$\Delta APQ\sim \Delta ARS\Rightarrow \frac{AP}{AR}=\frac{PQ}{SR}=\frac{AQ}{AS}$

AR=5AP

$\Rightarrow \frac{AP}{5AR}=\frac{PQ}{SR}\Rightarrow \frac{1}{5}=\frac{PQ}{SR}\Rightarrow SR=5PQ$