Question

$ABCD$ is a parallelogram and $AP$ and $CQ$ are perpendiculars from vertices $A$ and $C$ on diagonal $BD$. Then which of the following alternatives is correct?

• A. $AP=CQ$
• B. $AP=BC$
• C. $CQ=DA$
• D. $DQ=PB$

Answer 1

Answer: (A)

$AP=CQ$

In $△APB$ and $△CQD$

$\angle APB=\angle CQD={90}^{\circ }$

$\angle ABP=\angle CDQ$ {alternate opposite angle}

$AB=CD$ {Opoosite side of parallelogram are equal}

$△APB\cong △CQD$ [angle angle side]
$\therefore AP=CQ$ [CPCT]