Basic Mathematics for College Students

As figure (c) illustrates, points G, H,and Idetermine exactly one plane. In general,
any three different points determine exactly one plane.
Other geometric figures can be created by using parts or combinations of points,
lines, and planes.

9.1 Basic Geometric Figures; Angles 713

2 Identify and name line segments and rays.

Line Segment

The line segmentAB,written as , is the part of a line that consists of points

Aand Band all points in between (see the figure below). Points Aand Bare

the endpointsof the segment.

AB

Every line segment has a midpoint,which divides the segment into two parts of
equal length. In the figure below,Mis the midpoint of segment AB, because the
measure of , which is written as , is equal to the measure of which is
written as.

and

Since the measure of both segments is 3 units, we can write.
When two line segments have the same measure, we say that they are congruent.
Since , we can write

Read the symbol as “is congruent to.”

Another geometric figure is the ray, as shown below.

AM  MB

m(AM)m(MB)

m(AM)m(MB)

 3

m(MB) 7  4

 3

m(AM) 4  1

m(MB)

AM m(AM) MB

Line segment

Line segment AB is written as AB.

A

B

ABM

1234567

3 units 3 units

Ray

A rayis the part of a line that begins at some point (say,A) and continues

forever in one direction. Point Ais the endpointof the ray.

Ray

A

B

Ray AB is written as AB. The endpoint

of the ray is always listed first.

→

To name a ray, we list its endpoint and then one other point on the ray. Sometimes
it is possible to name a ray in more than one way. For example, in the figure on the
right, and name the same ray. This is because both have point Das their
endpoint and extend forever in the same direction. In
contrast, and are not the same ray. They have
different endpoints and point in opposite directions.

ED

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DE

¡

DF

¡

DE

¡

D E

F