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# In parallelogram ABCD, two points P and Q are taken on diagonal BD such that DP = BQ (see Fig. 8.20). Show that: (ii) AP = CQ

Q: 9     In parallelogram ABCD, two points P and Q are taken on diagonal BD such that  $\small DP=BQ$  (see Fig. $\small 8.20$). Show that:

(ii) $\small AP=CQ$

Views

Given: In parallelogram ABCD, two points P and Q are taken on diagonal BD such that $\small DP=BQ$.

To prove :$\small AP=CQ$

Proof :

In $\small \Delta APD\, \, and\, \, \Delta CQB,$

DP=BQ       (Given )

$\angle$ADP=$\angle$CBQ     (alternate angles)

AD=BC       (opposite sides of a parallelogram)

$\small \Delta APD\cong \Delta CQB$                (By SAS)

$\small AP=CQ$      (CPCT)

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