Download 2 and 3 Dimensional Figures

Standard 4.17a / Geometry
Page 1
Two and Three Dimensional Figures
Geometric figures are shapes that are either two- or three-dimensional. In math, we first
work with shapes that have two dimensions. We can easily draw two-dimensional
figures on a flat surface or plane.
Two-Dimensional Figures
Two-dimensional figures have only two dimensions: height and width.
A polygon is a two-dimensional figure that has straight sides and is closed. Polygon is a
word that comes from the Greek language and means “many” for “poly” and “angles” for
“gon.” All of the plane figures, which will be described in this notepage are polygons.
They include a triangle, a rectangle, a square, a rhombus, and a parallelogram. There are
many more, and a lot of them have the ending, “gon,” in their name, like pentagon. Have
you ever seen the building in Washington, D.C. called the Pentagon? It has five sides
and five angles.
A triangle is a polygon that has three sides and three angles. Both of these examples are
triangles. Even though the length of their sides and the sizes of their angles are different,
they both have three sides and three angles.
1
1
1
3
angles
2
sides
3
2
1
angles
3
2
3
2
A polygon with four sides is a quadrilateral. There are all kinds of quadrilaterals. One
type of quadrilateral is a rectangle. A rectangle has four right angles. In this example,
the small squares in the corners of the rectangle mean that the angles are right angles.
right angles
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Standard 4.17a / Geometry
Page 2
Two and Three Dimensional Figures
(continued)
Another quadrilateral is a square. A square is a rectangle with four sides of equal length.
If it is a rectangle, what kind of angles does a square have?
Another quadrilateral is a rhombus. Like a square, a rhombus has sides of equal length,
but there are no right angles. A rhombus looks like a square that leans. Is a rhombus a
rectangle?
The last kind of quadrilateral is a parallelogram. A parallelogram is a quadrilateral with
two sets of parallel sides. The opposite sides of a parallelogram are of equal length, and
the opposite angles of a parallelogram are the same size. A rectangle, a square, and a
rhombus are all parallelograms. They are called parallelograms because the opposite
sides are not just equal in length, but they are also parallel line segments. Parallel means
that the points of the line segments are always the same distance apart.
a
1

2
c

d
4
3
Sides a and b are parallel line segments.
Sides c and d are parallel line segments.
Angles 1 and 3 are the same size. Angles
2 and 4 are the same size.
b
We can put the properties of these quadrilaterals in a table to help remember them.
Name of figure
quadrilateral
rectangle
square
rhombus
parallelogram
Sides of equal
length
Parallel sides
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





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Right angles


Opposite
angles equal




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Standard 4.17a / Geometry
Page 3
Two and Three Dimensional Figures
(continued)
A circle is a closed curve with all of its points in one plane or flat surface. Each point on
a circle is the same distance from the center of the circle.
All points of the circle are equidistant
from the center.
center
Three-dimensional figures
It is important to identify and understand two-dimensional shapes in order to identify and
understand space figures or three-dimensional figures. Plane figures exist only on a flat
surface or plane. They have two dimensions of height and width. Three-dimensional
figures exist in space. They take up a different type of space than plane or twodimensional figures. Three dimensional figures haves height, width and depth.
depth
height
width
A sphere is a three-dimensional figure. All of the points of a sphere are the same
distance from its center. Any section cut across a sphere is a circle. A ball is a sphere.
Earth and other planets are in the shape of a sphere.

A cube is a three-dimensional solid figure. It has six congruent square faces and every
edge has the same length. Congruent means that the six faces of the cube are exactly the
same size and shape. A cube has 6 faces and 12 edges.
edge
face
© 2007
Standard 4.17a / Geometry
Page 4
Two and Three Dimensional Figures
(continued)
A rectangular prism is a three-dimensional solid figure. It has six rectangular faces and
12 edges. The edges of the rectangles do not have to be equal in length. The rectangles
that are opposite or across from each other are congruent and parallel to each other. How
many pairs of parallel, congruent faces can you find on this rectangle?
A cylinder is a three-dimensional object. It is formed by two congruent, parallel
circular bases joined by a curved surface. Think of the cardboard center of a paper towel
roll or the Styrofoam “noodles” we use at the pool or beach to help us swim. Most cans
are cylinder shaped.
circular base
A cone is a solid, pointed figure. It has a flat base that is usually a circle. This base is
joined to a vertex by a curved surface. The easiest way to picture a cone is an ice cream
cone or a party hat.
vertex
base
A square pyramid is a solid figure that has a square base. This base is joined to a vertex
by four triangular faces. Many people think of the pyramids in Egypt when describing
what this figure looks like.
vertex
triangular face
base
© 2007