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 about rectangles. 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/ |
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