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### 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

```
Associated Topics:
Middle School Geometry
Middle School Triangles and Other Polygons

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