Question

In the adjoining figure, $ABCD$ is a square of side $2cm$. Side $AB$ and $BC$ are produced to $P$ and $Q$ respectively such that $BP=CQ=1cm$. $AQ$ and $DP$ are joined. Is $AQ=DP$ ? Given reasons.

Answer 1

In $\Delta$ADP & $\Delta$BAQ

$AD=BC$(equal sides)

$\angle A=\angle B={90}^o$(square)

$AP=BQ=3$cm

By SAS property $\Delta ADP\cong \Delta BAQ$

Hence $AQ=DP$.