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ABCD is a parallelogram and AP and CQ are perpendiculars from vertices A and C on diagonal BD (see Fig. 8.21). Show that (ii) AP = CQ

Q: 10        ABCD is a parallelogram and AP and CQ are perpendiculars from vertices A and C on diagonal BD (see Fig. \small 8.21). Show that

                  (ii) \small AP=CQ

                    

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Given: ABCD is a parallelogram and AP and CQ are perpendiculars from vertices A  and C on diagonal BD.

To prove : \small AP=CQ

Proof: In\small \Delta APB\, \, and\, \, \Delta CQD,

           \angleAPB=\angleCQD             (Each 90 \degree)

           \angleABP=\angleCDQ            (Alternate angles)

               AB=CD                (Opposite sides of a parallelogram )

Thus, \small \Delta APB\cong \Delta CQD               (By SAS)

           \small AP=CQ                 (CPCT)

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