# Proving a figure in trapezium as parellologram

### Proving a figure in trapezium as parellologram

ABCD is a trapezium with AB parallel to CD. Angle bisector of A meets DC at P and angle bisector of C meets AB at Q. Prove that APCQ is a parellogram.
MV Rao
MV RAO

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### Re: Proving a figure in trapezium as parellologram

MV RAO wrote:ABCD is a trapezium with AB parallel to CD. Angle bisector of A meets DC at P and angle bisector of C meets AB at Q. Prove that APCQ is a parellogram.

let $$\angle{A}=2\alpha$$. AB||CD =>$$\angle{DPA}=\alpha$$. Analog, let $$\angle{BCD}=2\beta$$=>$$\angle{CQB}=\beta$$. we have to prove that $$\alpha+\beta=\pi$$.
i think this is not true

martin123456

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### Re: Proving a figure in trapezium as parellologram

martin123456 wrote:
MV RAO wrote:ABCD is a trapezium with AB parallel to CD. Angle bisector of A meets DC at P and angle bisector of C meets AB at Q. Prove that APCQ is a parallelogram.

let $$\angle{A}=2\alpha$$. AB||CD =>$$\angle{DPA}=\alpha$$. Analog, let $$\angle{BCD}=2\beta$$=>$$\angle{CQB}=\beta$$. we have to prove that $$\alpha+\beta=\pi$$.
i think this is not true

This is a text book problem for CBSE 8th standard in India. So I guess the problem is correct. To prove tha APCQ is a parallelogram, I believe if we can prove $$\alpha = \beta$$, it will be sufficient. How to prove it?

MV RAO

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### Re: Proving a figure in trapezium as parellologram

well, it is sufficient but not true, try drawing a trapezoid that fulfills the conditions given but APCQ not a parallelogram

martin123456

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