Basic Mathematics for College Students

Polygons are formed by fitting together line segments in such a way that

• no two of the segments intersect, except at their endpoints, and


• no two line segments with a common endpoint lie on the same line.
  The line segments that form a polygon
  are called its sides.The point where two sides
  of a polygon intersect is called a vertexof the
  polygon (plural vertices). The polygon shown
  to the right has 5 sides and 5 vertices.
  Polygons are classified according to the
  number of sides that they have. For example,
  in the figure below, we see that a polygon with four sides is called a quadrilateral,and
  a polygon with eight sides is called an octagon.If a polygon has sides that are all the
  same length and angles that are the same measure, we call it a regular polygon.

736 Chapter 9 An Introduction to Geometry

SECTION 9.3

Triangles

Objectives

1 Classify polygons.

2 Classify triangles.

3 Identify isosceles triangles.

4 Find unknown angle measures

of triangles.

We will now discuss geometric figures called polygons.We see these shapes every day.

For example, the walls of most buildings are rectangular in shape. Some tile and vinyl

floor patterns use the shape of a pentagon or a hexagon. Stop signs are in the shape of

an octagon.

In this section, we will focus on one specific type of polygon called a triangle.

Triangular shapes are especially important because triangles contribute strength and

stability to walls and towers. The gable roofs of houses are triangular, as are the sides

of many ramps.

© William Owens/Alamy

The House of the Seven

Gables, Salem, Massachusetts

1 Classify polygons.

Polygon

A polygonis a closed geometric figure with at least three line segments for its

sides.

Vertex

Vertex

Vertex

Vertex

Vertex

Side

Side

Side

Side

Side

Triangle

3 sides

Quadrilateral

4 sides

Pentagon

5 sides

Hexagon

6 sides

Heptagon

7 sides

Polygons

Octagon

8 sides

Nonagon

9 sides

Decagon

10 sides

Dodecagon

12 sides

Regular

polygons

EXAMPLE (^1) Give the number of vertices of:
a.a triangle b.a hexagon
StrategyWe will determine the number of angles that each polygon has.
WHYThe number of its vertices is equal to the number of its angles.
Self Check 1
Give the number of vertices of:
a.a quadrilateral
b.a pentagon
Now TryProblems 25 and 27