Suppose you have actually a polygon, like probably a triangle or a rectangle, and you clone it. Currently you have two congruent polygon lying next by side. If your polygons don" acquire along, and also the airplane isn" large enough because that the both the them, among them will have to move. Go ahead and move among your polygons into a new plane. Don" twisted it, or revolve it, or rotate it in any kind of way. Simply lift the (or reduced it, if you" prefer) to a brand-new plane the is parallel come the old plane. It doesn" need to be straight over (or under, if you decided to reduced it) the various other polygon; you can move it party if the heart moves you. The score is to have actually the two polygons in parallel planes, v the same orientation.

You are watching: Any polygon can be the base of a prism

It" a well-known truth that lack makes the heart thrive fonder. Currently that your polygons have been separated, they might miss every other. That" no to say the they want to live in the same airplane again. They could just desire to develop some type of connection. After all, these are congruent polygons, and the corresponding vertices could want to maintain their connection. Let" draw line segment connecting each pair of corresponding vertices. The an outcome is a ?solid? number known together a prism. 2 prisms (one based on a triangle, the other based upon a rectangle) are displayed in number 21.1. An alert that the two polygons lied in parallel planes.


Figure 21.1Two examples of prisms.

In order to talk about this brand-new shape, I require to present you to some terms for the components of a prism. The congruent polygons the lie in the parallel planes are the bases that the prism, and also sides of this polygons are called the base edges. The line segments that affix the matching vertices the the congruent polygon are dubbed the lateral edges of the prism. The polygons the are formed by the lateral edges are called the lateral faces of the prism. The vertices of the congruent polygons room the vertices the the prism. A prism will constantly have double as numerous vertices as the base polygon.


A prism is the an ar formed by two parallel congruent polygons having matching vertices joined by heat segments.

The bases of a prism room the congruent polygons the lie in the parallel planes.

The base edges of a prism space the edges of the basic of the prism.

A vertex of a prism is a allude of intersection of 2 base edges.

The lateral edges that a prism are the heat segments connecting corresponding vertices of the bases of the prism.

A lateral face of a prism is the quadrilateral developed by a pair of equivalent base edges and the lateral edge that attach the matching vertices.

In the triangular prism, among the two congruent triangles is straight over the various other one. In this case the lateral edges room perpendicular to the basic edges, and the prism is referred to as a ideal prism. If the bases of a appropriate prism are consistent polygons (recall the a regular polygon is an equilateral and equiangular polygon), climate the prism is dubbed a consistent prism.

In the rectangle-shaped prism (the prism developed from congruent rectangles) presented in figure 21.1, the lateral edges are not perpendicular come the basic edges. This is an example of an tilt prism.

By now you could have noticed that a prism" surname is regarded the shape of its base. A triangular prism has a triangular base; a rectangle-shaped prism has actually a rectangular base, and so on. This pattern will certainly be complied with to the finish of time (or at the very least until your capability to name polygons expires).

Solid facts

A right prism is a prism in i beg your pardon the lateral edges are perpendicular come the basic edges at the vertices.

An oblique prism is a prism in i m sorry the angle formed in between a lateral edge and also a base edge is not a best angle.

A regular prism is a appropriate prism whose basic is a continual polygon.

The most familiar prism is a cube. A cube is a prism through a square base. But that" just the beginning! The lateral edges of a cube are perpendicular come the base edges, so a cube is a best prism. But wait! There" more! The bases that a cube are squares, which are continuous polygons. For this reason a cube is a right prism whose basic is a continuous polygon. In other words, a cube is a consistent prism. Yet there" more to a cube 보다 that. A cube has lateral edges that space the same size as the basic edges. That" enough to placed a cube into a very elite category. It" in such an elite course that there are only 5 shapes worthy that admission. You" learn more about that course at the finish of this section.


To name a prism, start with the surname of the polygon that forms its base. Next, identify if the basic of the prism is a consistent polygon. If the is, you have a constant prism. If not, girlfriend just have a run-of-the-mill, generic prism. Finally, recognize if the lateral edges space perpendicular come the basic edges. If castle are, you have a best prism; otherwise you have actually an slope prism. Put every one of the pieces together and also you have actually named that prism.

Prisms room named and also classified by your bases and the relationship between their lateral edges and their basic edges. Let" practice.

Example 1: Name and classify each type of prism shown in number 21.2.

Figure 21.2Three prisms to name and classify.

Solution: The very first prism has actually a hexagonal base (not equilateral) and lateral edges perpendicular come the base edges. That provides it a appropriate hexagonal prism. The second prism has a pentagonal basic (not equilateral) and the lateral edges space not perpendicular come the base, therefore it" an oblique pentagonal prism. The third prism has a triangular base, and also it is equilateral. By to organize 14.3 the is also equiangular, which provides it regular. Because the lateral edges are perpendicular come the basic edges, that is a ideal prism. For this reason it is a right, regular, triangular prism.

Excerpted from The complete Idiot" overview to Geometry 2004 by Denise Szecsei, Ph.D.. All legal rights reserved including the ideal of reproduction in entirety or in part in any kind of form. Supplied by plan with Alpha Books, a member of Penguin group (USA) Inc.

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