Download Section 9.1

Chapter Nine
Geometry and Measurement
Section 9.1
Lines and Angles
A plane is a flat surface that extends
indefinitely.
Plane
Space extends in all directions
indefinitely.
Martin-Gay, Prealgebra, 5ed
3
Point
The most basic concept of geometry is
the idea of a point in space. A point has
no length, no width, and no height, but it
does have location. We will represent a
point by a dot, and we will label points
with letters.
A
Point A
Martin-Gay, Prealgebra, 5ed
4
Line AB or AB
A
B
Line Segment AB or AB
A
B
Ray AB or AB
A
B
Martin-Gay, Prealgebra, 5ed
5
An angle is made up of two rays that share
the same endpoint called a vertex.
A
Vertex
B
x
C
The angle can be named ABC, CBA, B,
or x.
The vertex is the
middle point.
6
An angle can be measured in degrees.
There are 360º (degrees) in a full
revolution or full circle.
360º
Martin-Gay, Prealgebra, 5ed
7
Classifying Angles
Name
Angle Measure
Acute
Angle
Between 0° and 90°
Right
Angle
Exactly 90°
Obtuse
Angle
Between 90° and 180°
Straight
Angle
Exactly 180º
Examples
8
Two angles that have a sum of 90° are
called complementary angles.
Two angles that have a sum of 180° are
called supplementary angles.
Martin-Gay, Prealgebra, 5ed
9
Two lines in a plane can be either parallel or
intersecting. Parallel lines never meet.
Intersecting lines meet at a point. The symbol
 is used to denote “is parallel to.”
p
q
Parallel lines
p  q
Intersecting
lines
Martin-Gay, Prealgebra, 5ed
10
Two lines are perpendicular if they form right
angles when they intersect. The symbol  is
used to denote “is perpendicular to.”
Perpendicular lines
m
n
nm
Martin-Gay, Prealgebra, 5ed
11
When two lines intersect, four angles are formed.
Two of these angles that are opposite each other
are called vertical angles. Vertical angles have the
same measure.
a
d
b
c
a = c
d = b
Martin-Gay, Prealgebra, 5ed
12
Two angles that share a common side are
called adjacent angles. Adjacent angles formed
by intersecting lines are supplementary. That is,
they have a sum of 180 °.
a
d
b
c
a and b
b and c
c and d
d and a
Martin-Gay, Prealgebra, 5ed
13
A line that intersects two or more lines at
different points is called a transversal.
Martin-Gay, Prealgebra, 5ed
14
Parallel Lines Cut by a Transversal
If two parallel lines are cut by a
transversal, then the measures of
corresponding angles are equal and
alternate interior angles are equal.
Martin-Gay, Prealgebra, 5ed
15
Corresponding angles are equal.
a b
c d
e f
g h
a =  e
b = f
c = g
d = h
Martin-Gay, Prealgebra, 5ed
16
Alternate interior angles are angles on
opposite sides of the transversal between
the two parallel lines.
a b
c d
e f
g h
c = f
d = e
Martin-Gay, Prealgebra, 5ed
17