Basic Mathematics for College Students

812 Chapter 9 An Introduction to Geometry

An angleis a figure formed by two rays (called sides)

with a common endpoint. The common endpoint is

called the vertexof the angle.

We read the symbol as “angle.”

The angle below can be written as BAC,CAB,A, or  1.

When two angles have the same measure, we say that

they are congruent.

A protractoris used to find the measure of an angle.

One unit of measurement of an angle is the degree.

The notation is read as “the measure of

DEF.”

m(DEF)

An acute anglehas a measure that is greater than 0°

but less than 90°. An obtuse anglehas a measure that

is greater than 90° but less than 180°. A straight angle

measures 180°.

A right anglemeasures 90°.

Since m(DEF)  m(STV), we say that DEF  STV.

60°

Congruent

angles

60°

E T

FV

DS

40 °

Acute angle

130 °

Obtuse angle

180 °

Straight angle

The sumof the measures of the two adjacent angles is 32°:

The word sumindicates addition.

Subtract 21° from both sides.

Do the subtraction.

Thus, is 11°.x

x11°

x21°21°32°21°

x21°32°

We can use the algebra concepts of variable and

equation to solve many types of geometry problems.

A line segmentis a part of a line with two endpoints.

Every line segment has a midpoint,which divides the

segment into two parts of equal length.

The notation is read as “the measure of line

segment .”

When two line segments have the same measure, we

say that they are congruent.Read the symbol as “is

congruent to.”

A rayis a part of a line with one endpoint.



AM

m(AM)

B

M

A

endpoint

endpoint

endpoint

midpoint

Line segment AB

D

C

Ray CD

m(AM)  m(MB)

AM  MB

A

B

C

1

Vertex of

the angle

Sides of

the angle

Angle

A symbol is

often used to

90 ° label a right angle.

Right angle

Two angles that have the same vertex and are side-

by-side are called adjacent angles.

Two angles with degree measures of

and 21° are adjacent angles, as shown

here. Use the information in the figure to

find .x

x

x

32 °

21 °

Adjacent angles