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Prisms

A prism is a polyhedron whose faces consist of two
congruent
polygons lying in
parallel
planes and a number of
parallelograms. The
sides of the parallelograms are the
segments
that join the corresponding vertices of the two
congruent polygons. These two congruent polygons are called the
*bases* of
the prism. The parallelograms are called the *lateral faces* of
the prism.
The segments that join the bases and form the sides of the lateral faces are
called the lateral edges of the prism. The union of the two polygons and
the parallelograms form the entire prism.

Some obvious questions come up at this point. How many lateral faces are in a
prism? The number of lateral faces is equal to the number of sides in the
bases. If the bases are quadrilaterals, for
example, then there will be four lateral faces. Why are the lateral faces
parallelograms? The reason is that the bases lie in parallel planes. The
segments joining them (the sides of the lateral faces), are parallel to each
other, and the sides of the congruent polygons are parallel to each other. A
pair of segments and a pair of sides make up the sides of the lateral faces, so
each lateral face is a parallelogram.

Figure %: A prism

In the figure above, the polygons ABCDE and FGHIJ are the bases of the prism.
They are congruent and lie in parallel planes. The lateral faces, like
quadrilateral JEDI, for example, are parallelograms.

One special kind of prism is a right prism. In a right prism, the lateral
faces are all rectangles, and the lateral edges are
perpendicular to the planes that contain the
bases. One example of a right prism is a cube. A cube is a six-sided
polyhedron whose faces are all congruent squares.
Below a right prism is drawn:

Figure %: A right prism

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Cylinders

Prisms are only one member in a larger group of geometric surfaces. That
larger group is the set of cylinders. A cylinder is a surface that consists
of two congruent simple closed curves lying in
parallel planes and the segments that connect them. If these simple closed
curves were polygons, then the cylinder would be a prism. Here is a drawing of
a cylinder.

Figure %: A cylinder

The parallel simple closed curves are the

*bases* of the
cylinder, and the
segments that complete the cylinder form the

*lateral surface.*
Each segment
in the lateral surface lies in a line, and
each of these lines is parallel to the others that span the lateral surface.
For example, in the figure above, the segment AB lies in a line that is parallel
to the line that contains the segment BC. All of the segments that compose the
lateral surface lie in such parallel lines.

We've already talked about cylinders whose bases are polygons. Another kind of
cylinder with a special base is a circular cylinder. As you may have
already guessed, a circular cylinder is a cylinder with
circular bases. In addition to that, a right
circular cylinder is a circular cylinder whose lateral surface contains
segments that are perpendicular to the bases. A right circular cylinder is
drawn below.

Figure %: A right circular cylinder

A prism is one of the most basic polyhedrons, as well as an interesting example
of a cylinder.