# Thread: Proving angles are equal if bisectors are parallel

1. ## Proving angles are equal if bisectors are parallel

The question asks that if there's a parallelogram ABCD and bisectors of < ABC and < ADC are parallel then how can we prove that angles <DAB and <BCD are equal.

I have managed to work backwards and show that triangle DAE and FBC both have the same angles by working with the parallel lines. I have simply sketched in the angles congruent to <DAE and <BCF and gone from there. I let E be the point where the bisector from angle <DAB met the opposite side and F be the point at which the bisectors from <DCB touched the opposite side. How do I prove that it because the proof is dependent on the placement of E and F, That in all cases this will work?

2. ## Re: Proving angles are equal if bisectors are parallel

Hello, Idiotinabox!

Is there a typo in the problem?

$\text{Given: parallelogram }ABCD\text{ and bisectors of }\angle ABC\text{ and }\angle ADC\text{ are parallel.}$
$\text{Prove that: }\:\angle DAB \:=\: \angle BCD.$

In any parallelogram, opposite angles are always equal.
It has nothing to do with angle bisectors.

Code:
           B               C
* - - - - - - *
/           θ /
/             /
/             /
/             /
/ θ           /
* - - - - - - *
A               D

3. ## Re: Proving angles are equal if bisectors are parallel

Problem makes sense if the opposite angle theorem of parallelograms is not allowed

4. ## Re: Proving angles are equal if bisectors are parallel

Sorry, it's not a parallelogram. My mistake

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# prove that the bisector of opposite angles of a parellogrm are parallel

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