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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: (iii) ∆ AQB ≅ ∆ CPD

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:

 \small \Delta AQB\cong \Delta CPD

 

Answers (1)

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

To prove :\small \Delta AQB\cong \Delta CPD

Proof :

In \small \Delta AQB\, \, and\, \, \Delta CPD,

DP=BQ       (Given )

 \angleABQ=\angleCDP (alternate angles)

AB=CD       (opposite sides of a parallelogram)

\small \Delta AQB\cong \Delta CPD   (By SAS)

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