Question

ABCD is a parallelogram and AP and CQ are perpendiculars from vertices A and C on diagonal BD (See the given figure). Then,

• A. $\Delta ADB\cong \Delta CQD$
• B. $AP=CQ$
• C. $BP=DQ$
• D. None of these

Answer 1

Answer: (B), (C)

The correct options are
B

$AP=CQ$

C

$BP=DQ$

ABCD is a parallelogram (given)
In$△APD$ and $△CQB$
$\left(i\right)AD=BC$...(ABCD is a paralleligram)
$\left(ii\right)\angle APD=\angle CQB={90}^{\circ }$ ...(given)
$\left(iii\right)\angle ADP=\angle CBQ$ ...(alternate angles)
$\left(iv\right)△APD\cong △CQB$ ...(AAS Postulate)
$\left(v\right)AP=CQ$ ...(cpct)
$\left(vi\right)DP=BQ$ ...(cpct)
Adding PQ to both sides we get,
DP+PQ=BQ+QP
DQ=BP