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It seems to be the case that if \(AB=BC=CD\) and \(\angle ABC+\angle BCD = 240^{\circ}\), then the angle bisectors of \(\angle ABC\) and \(\angle BCD\) intersect on \(\overline{AD}\). Can someone prove or disprove this?

 

Edit: I forgot to mention that ABCD must be a quadrilateral.

 Dec 18, 2018
edited by Guest  Dec 18, 2018
 #1
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I am going to try to draw a diagram, but I am not 100% sure if it is the correct shape. Usually, for geometry, we prove things correct, unless it is an indirect proof, then we prove the conclusion wrong and work towards the true conclusion. 

 Dec 18, 2018
 #2
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It seems fairly clear from the following diagram that it is not always true.  The specified angle bisectors clearly won't intersect on AD. 

 

The proposition may well be true for a non-intersecting diagram.

 

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 Dec 18, 2018
 #3
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Sorry, I think I need to say that ABCD must be a quadrilateral. Is it always true when that is the case?

Guest Dec 18, 2018

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