Supplementary Angles in a ParallelogramDate: 10/23/95 at 13:40:49 From: Anonymous Subject: Geometry Are all parallelograms supplementary? Date: 11/3/95 at 15:33:20 From: Doctor Ken Subject: Re: Geometry Hello! I'm not exactly sure what you would mean by a "supplementary" parallelogram, because when we talk about things being supplementary, we're usually talking about two angles. But I suppose you may mean that a quadrilateral is supplementary iff (if and only if) every pair of adjacent angles is supplementary. In fact, that is true in every parallelogram. The way you could show it is to extend the four sides of the parallelogram to complete lines (instead of line segments), and then look for transversals of parallel lines. Do you know the theorem that says that "alternate interior angles" are congruent? Well, that would really come in handy here. See if you can work this out, and if you're still confused, please write back to us. -Doctor Ken, The Geometry Forum |
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