# 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

Posts: 7
Joined: Wed Dec 09, 2009 5:01 am

### 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

Posts: 12
Joined: Tue Nov 17, 2009 10:15 am

### 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

Posts: 7
Joined: Wed Dec 09, 2009 5:01 am

### 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

Posts: 12
Joined: Tue Nov 17, 2009 10:15 am