Question

In the parallelogram ABCD, CP and DP are bisectors of angles C and D. Prove that angle DPC = 90 and AB =PB

Answer 1

Answer:

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Answer 2

Given,

Parallelogram ABCD

Bisector of ∠C & ∠D= CP & DP

To find,

∠DPC=90°

AB=PB

Solution,

Given, AB & PB are bisectors of parallelogram ABCD

Therefore, two triangles ΔADP & ΔBCP are formed.

Angle A = Angle B = 90° (property of parallelogram)

Angle D= Angle C (since DP & CP are bisectors)

AD=CD(sides of parallelogram)

so, by ASA config. condition ΔADP is congruent to ΔBCP

Therefore, by C.P.C.T

AP=BP.

Hence, proved.