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

                  (i) \small \Delta APB\cong \Delta CQD

                    

Answers (1)

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

To prove : \small \Delta APB\cong \Delta CQD

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)

 

 

 

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