Proving a figure in trapezium as parellologram

by **MV RAO** » Wed Dec 09, 2009 5:10 am

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.

by **martin123456** » Thu Dec 10, 2009 1:45 pm

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

by **MV RAO** » Thu Dec 10, 2009 11:25 pm

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?

by **martin123456** » Fri Dec 11, 2009 8:28 am

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

Proving a figure in trapezium as parellologram

Proving a figure in trapezium as parellologram

Re: Proving a figure in trapezium as parellologram

Re: Proving a figure in trapezium as parellologram

Re: Proving a figure in trapezium as parellologram

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