Question

In quadrilateral $ABCD,AD=BC$ and $AP=QB$. $DP$ and $CQ$ are perpendiculars on the segment $AB$ from points $D$ and $C$ respectively. If $DP=6cm$ find the length of $CQ$.

Answer 1

Here, $ABCD$ is a quadrilateral, where $DP$ and $CQ$ are perpendiculars on the segment $AB.$

In $△APD$ and $△BQC$

$\Rightarrow$ $AD=BC$ [ Given ]

$\Rightarrow$ $AP=QB$ [ Given ]

$\Rightarrow$ $\angle APD=\angle BQC$ [ Both are ${90}^o.$ ]

$\therefore$ $△APD\cong △BQC$ [ By $SSA$ congruence theorem ]

$\Rightarrow$ $DP=CQ$ [ CPCT ]

$\Rightarrow$ $DP=6cm$ [ Given ]

$\therefore$ $CQ=6cm$