Basic Mathematics for College Students

Triangles may also be classified by their angles, as shown below.

738 Chapter 9 An Introduction to Geometry

Right triangle

(has one right angle)

Obtuse triangle

(has an obtuse angle)

Acute triangle

(has three acute angles)

(a)

Right triangles

Leg

Leg

Hypotenuse

(b)

Right triangles have many real-life applications. For example, in figure (a) below,

we see that a right triangle is formed when a ladder leans against the wall of a building.

The longest side of a right triangle is called the hypotenuse,and the other two

sides are called legs.The hypotenuse of a right triangle is always opposite the 90°

(right) angle. The legs of a right triangle are adjacent to (next to) the right angle, as

shown in figure (b).

3 Identify isosceles triangles.

In an isosceles triangle, the angles opposite the sides of equal length are called base

angles,the sides of equal length form the vertex angle,and the third side is called the

base.Two examples of isosceles triangles are shown below.

Isosceles triangles

Base angle Base angle

Base

Vertex angle

Base angle Base angle

Base

Vertex angle

We have seen that isosceles triangles have two sides of equal length. The isosceles

triangle theoremstates that such triangles have one other important characteristic:

Their base angles are congruent.

Isosceles Triangle Theorem

If two sides of a triangle are congruent, then the angles opposite those sides

are congruent.