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:

              (iv) \small AQ=CP

                

Answers (1)

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

To prove :\small AQ=CP 

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)          

   \small AQ=CP                       (CPCT)

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