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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

             

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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 AP=CQ

Proof :

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

   DP=BQ       (Given )

 \angleADP=\angleCBQ     (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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