Notes Three-Dimensional Figures, Summaries of Geometry

A prism is a three-dimensional figure with two parallel, congruent bases. The bases, which are also two of the faces, can be any polygon.

Typology: Summaries

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Notes Three-Dimensional Figures
How Can You Classify Three-Dimensional Figures?
You can classify three-dimensional figures based on information about their faces, bases, edges,
and vertices. Three-dimensional figures include prisms and pyramids, as well as figures with
curved surfaces.
A prism is a three-dimensional figure with two parallel, congruent bases. The bases, which are
also two of the faces, can be any polygon. The other faces are rectangles. A prism is named
according to the shape of its bases.
A pyramid is a three-dimensional figure with only one base. The base can be any polygon. The
other faces are triangles. A pyramid is named according to the shape of its base.
Here are some three-dimensional figures with which you should be familiar:
Prisms & Pyramids
Type
Examples
Properties
Triangular Prism
โ— 5 faces
2 triangular bases
3 rectangular faces
โ— 9 edges
โ— 6 vertices
Rectangular Prism
โ— 6 faces
2 rectangular bases
4 rectangular faces
โ— 12 edges
โ— 8 vertices
Cube
โ— 6 faces
2 square bases
4 square faces
โ— 12 edges
โ— 8 vertices
Square Pyramid
โ— 5 faces
1 square base
4 triangular faces
โ— 8 edges
โ— 5 vertices
Triangular Pyramid
โ— 4 faces
1 triangular base
3 triangular faces
โ— 6 edges
โ— 4 vertices
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Notes Three-Dimensional Figures

How Can You Classify Three-Dimensional Figures?

You can classify three-dimensional figures based on information about their faces, bases, edges,

and vertices. Three-dimensional figures include prisms and pyramids, as well as figures with

curved surfaces.

A prism is a three-dimensional figure with two parallel, congruent bases. The bases, which are

also two of the faces, can be any polygon. The other faces are rectangles. A prism is named

according to the shape of its bases.

A pyramid is a three-dimensional figure with only one base. The base can be any polygon. The

other faces are triangles. A pyramid is named according to the shape of its base.

Here are some three-dimensional figures with which you should be familiar:

Prisms & Pyramids

Type Examples Properties Triangular Prism โ— 5 faces 2 triangular bases 3 rectangular faces โ— 9 edges โ— 6 vertices Rectangular Prism โ— 6 faces 2 rectangular bases 4 rectangular faces โ— 12 edges โ— 8 vertices Cube โ— 6 faces 2 square bases 4 square faces โ— 12 edges โ— 8 vertices Square Pyramid โ— 5 faces 1 square base 4 triangular faces โ— 8 edges โ— 5 vertices Triangular Pyramid โ— 4 faces 1 triangular base 3 triangular faces โ— 6 edges โ— 4 vertices

You should also be familiar with three-dimensional figures that have curved surfaces. These

figures include cylinders, cones, and spheres. You can classify these three-dimensional figures

based on information about their bases and surfaces.

Three Dimensional Figures with Curved Surfaces

Type Example Properties

Cylinder

โ— 2 circular bases โ— 1 curved surface

Cone

โ— 1 circular base โ— 1 curved surface โ— 1 vertex

Sphere

โ— 1 curved surface