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Math Help - Proving angles are equal if bisectors are parallel

  1. #1
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    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?
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  2. #2
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    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
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  3. #3
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    Re: Proving angles are equal if bisectors are parallel

    Problem makes sense if the opposite angle theorem of parallelograms is not allowed
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  4. #4
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    Re: Proving angles are equal if bisectors are parallel

    Sorry, it's not a parallelogram. My mistake
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