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### What Constitutes a Prism?

```
Date: 06/10/99 at 17:48:54
From: Kelsey Sullivan
Subject: Geometry, 3-D objects

If I am looking at a 3-dimensional object that's shaped like a
triangle, how do I know if it's a prism? I have the same question

Sincerely,
Kelsey
```

```
Date: 06/11/99 at 12:16:44
From: Doctor Peterson
Subject: Re: Geometry, 3-D objects

Hi, Kelsey.

You can think of a prism this way: Take any polygon, such as a
triangle or rectangle, and imagine holding it flat while moving it
straight in some direction. Now imagine that wherever it goes it
leaves a trail in the air. The shape you get will be a prism:

Move this shape in the direction shown

\
\
+---\----------------------+
/......\.................../
/.........\................/
/............\............./
/........................../
/........................../
+--------------------------+

and it makes this prism:

+--------------------------+
/........................../  \
/........................../     \
/........................../        \
/........................../           \
/........................../              \
+--------------------------+                 \
\                 \        \                 \
\                 +--------\-----------------+
\              /...........\............. /
\           /..............\.........../
\        /.................\......../
\     /....................\...../
\  /.......................\../
+--------------------------+

So if two opposite faces are parallel and congruent (the same shape
and size), and the edges connecting corresponding vertices (corners)
of these faces are all parallel, then it is a prism. The
parallelepiped above is a kind of prism; if you replace the shaded
parallelograms with any polygon, it will still be a prism. Here's a
triangular prism:

+-----------------------------------+
|  \............................./  |
|     \......................./     |
|        \................./        |
|           \.........../           |
|              \...../              |
|                 +                 |
|                 |                 |
|                 |                 |
|                 |                 |
|                 |                 |
|                 |                 |
|                 |                 |
|                 |                 |
|                 |                 |
|                 |                 |
+-----------------|-----------------+
\..............|............../
\...........|.........../
\........|......../
\.....|...../
\..|../
+

You can see some pictures of different prisms on our FAQ page:

http://mathforum.org/dr.math/faq/formulas/faq.prism.html

- Doctor Peterson, The Math Forum
http://mathforum.org/dr.math/
```
Associated Topics:
High School Definitions
High School Geometry
High School Higher-Dimensional Geometry

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