Question

ABCD is a parallelogram the bisectors of the angles A and B meet the diagonal BD in P and Q respectively. Prove that ΔAPB ≈ ΔCQD .


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Answer 1

Answer:

ABCD is a parallelogram and AP and CQ are perpendicular from vertices A and C are diagonals BD show that,

1. ∆APB = ∆CAD

2.AP =CQ

soln.

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

To prove,

1.∆ APB = ∆ CAD

2. AP =CQ

proof:

1. In ∆ APB and ∆ CQD we have,

∆ABP = ∆CQD [ Alternative angle]

AB= CD [opposite side of a parallelogram]

∆ APB = ∆ CQD [ each =90°]

Hence, ∆ APB = ∆ CQD [ ASA congruence]

2. so, AP=CQ [CPCT]

Hence, be proved...

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