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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 (i) ∆ APB ≅ ∆ CQD

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 \small \Delta APB\cong \Delta CQD

  

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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 \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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