Question

In parallelogram ABCD, two points P and Q are taken on diagonal BD such that DP=BQ (see the given figure) Show that:
AP = CQ

Answer 1

In $\Delta APDand\Delta CQB$,
$\angle ADP=\angle CBQ$
(Alternate interior angles)

AD =CB (Opposite sides of parallelogram ABCD)
DP=BQ (Given)

$\therefore \Delta APD\cong \Delta CQB$
(using SAS congruence rule)

As we have proved that triangle APD is congruent to triangle CQB,
Hence, AP= CQ (CPCT)