Basic Mathematics for College Students

Many scholars consider Euclid(330?–275? BCE) to be the greatest of the Greek

mathematicians. His book The Elementsis an impressive study of geometry and

number theory. It presents geometry in a highly structured form that begins with

several simple assumptions and then expands on them using logical reasoning. For

more than 2,000 years,The Elementswas the textbook that students all over the world

used to learn geometry.

712 Chapter 9 An Introduction to Geometry

SECTION 9.1

Basic Geometric Figures; Angles

Objectives

1 Identify and name points, lines,

and planes.

2 Identify and name line

segments and rays.

3 Identify and name angles.

4 Use a protractor to measure

angles.

5 Solve problems involving

adjacent angles.

6 Use the property of vertical

angles to solve problems.

7 Solve problems involving

complementary and

supplementary angles.

Geometry is a branch of mathematics that studies the properties of two- and three-

dimensional figures such as triangles, circles, cylinders, and spheres. More than 5,000

years ago, Egyptian surveyors used geometry to measure areas of land in the flooded

plains of the Nile River after heavy spring rains. Even today, engineers marvel at the

Egyptians’ use of geometry in the design and construction of the pyramids. History

records many other practical applications of geometry made by Babylonians, Chinese,

Indians, and Romans.

The Language of Mathematics The word geometrycomes from the Greek

words geo(meaning earth) and metron(meaning measure).

1 Identify and name points, lines, and planes.

Geometry is based on three undefined words:point, line,and plane.Although we will

make no attempt to define these words formally, we can think of a pointas a geometric

figure that has position but no length, width, or depth. Points can be represented on

paper by drawing small dots, and they are labeled with capital letters. For example,

point Ais shown in figure (a) below.

(a)

Point Line Plane

(b)

(c)

A

B

I

G

H

C

E

F

Line BC is written as BC

Points are labeled

with capital letters.

Lines are made up of points. A line extends infinitely far in both directions, but

has no width or depth. Lines can be represented on paper by drawing a straight line

with arrowheads at either end. We can name a line using any two points on the line. In

figure (b) above, the line that passes through points Band Cis written as.

Planes are also made up of points. A plane is a flat surface, extending infinitely far

in every direction, that has length and width but no depth. The top of a table, a floor,

or a wall is part of a plane. We can name a plane using any three points that lie in the

plane. In figure (c) above, lies in plane GHI.

As figure (b) illustrates, points Band Cdetermine exactly one line, the line.

In figure (c), the points Eand Fdetermine exactly one line, the line. In general,

any two different points determine exactly one line.

EF

·

BC

·

EF

·

BC

·

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