Supplementary Angles in a Parallelogram

Date: 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