Basic Mathematics for College Students

9.3 Triangles 737

Solution
a.From the figure on the previous page, we see that a triangle has three angles
and therefore three vertices.

b.From the figure on the previous page, we see that a hexagon has six angles and
therefore six vertices.

Success Tip From the results of Example 1, we see that the number of vertices

of a polygon is equal to the number of its sides.

2 Classify triangles.

A triangleis a polygon with three sides (and three vertices). Recall that in geometry
points are labeled with capital letters. We can use the capital letters that denote the
vertices of a triangle to name the triangle. For example, when referring to the triangle
in the right margin, with vertices A, B,and C,we can use the notation (read as
“triangle ABC”).

ABC

The Language of Mathematics When naming a triangle,

we may begin with any vertex. Then we move around the

figure in a clockwise (or counterclockwise) direction as we

list the remaining vertices. Other ways of naming the triangle

shown here are ACB,,,BCABACCAB, and .CBA

The Language of Mathematics The figures below show how triangles can be

classified according to the lengths of their sides. The single tick marksdrawn

on each side of the equilateral triangle indicate that the sides are of equal

length. The double tick marks drawn on two of the sides of the isosceles

triangle indicate that they have the same length. Each side of the scalene

triangle has a different number of tick marks to indicate that the sides have

different lengths.

The Language of Mathematics Since every angle of an equilateral triangle

has the same measure, an equilateral triangle is also equiangular.

The Language of Mathematics Since equilateral triangles have at least two

sides of equal length, they are also isosceles. However, isosceles triangles are

not necessarily equilateral.

Equilateral triangle

(all sides equal length)

Isosceles triangle

(at least two sides of

equal length)

Scalene triangle

(no sides of equal length)

AB

C