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Chapter 8
Geometry and
Measurement
Copyright © 2011 Pearson Education, Inc. Publishing as Prentice Hall.
8.1
Lines and Angles
Copyright © 2011 Pearson Education, Inc. Publishing as Prentice Hall.
Planes
A plane is a flat surface that extends indefinitely.
Plane
Space extends in all directions indefinitely.
Copyright © 2011 Pearson Education, Inc. Publishing as Prentice Hall.
Martin-Gay, Prealgebra & Introductory Algebra, 3ed
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Points
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
Copyright © 2011 Pearson Education, Inc. Publishing as Prentice Hall.
Martin-Gay, Prealgebra & Introductory Algebra, 3ed
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Lines, Segments, and Rays
A
Line AB or AB
B
Line Segment AB or AB
A
B
Ray AB or AB
A
B
Copyright © 2011 Pearson Education, Inc. Publishing as Prentice Hall.
Martin-Gay, Prealgebra & Introductory Algebra, 3ed
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Angles
An angle is made up of two rays that share the same
endpoint called the vertex.
A
Vertex
x
B
C
The angle can be named ABC, CBA, B, or x.
The vertex is the
middle point.
Copyright © 2011 Pearson Education, Inc. Publishing as Prentice Hall.
Martin-Gay, Prealgebra & Introductory Algebra, 3ed
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Angles
An angle can be measured in degrees. There are
360º (degrees) in a full revolution or full circle.
360º
Copyright © 2011 Pearson Education, Inc. Publishing as Prentice Hall.
Martin-Gay, Prealgebra & Introductory Algebra, 3ed
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Classifying Angles
Name
Angle Measure
Acute Angle
Between 0° and 90°
Right Angle
Exactly 90°
Obtuse
Angle
Straight
Angle
Examples
Between 90° and 180°
Exactly 180º
Copyright © 2011 Pearson Education, Inc. Publishing as Prentice Hall.
Martin-Gay, Prealgebra & Introductory Algebra, 3ed
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Classifying Angles
Two angles that have a sum of 90° are called
complementary angles.
Two angles that have a sum of 180° are called
supplementary angles.
Copyright © 2011 Pearson Education, Inc. Publishing as Prentice Hall.
Martin-Gay, Prealgebra & Introductory Algebra, 3ed
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Parallel Lines
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
Intersecting lines
p  q
Copyright © 2011 Pearson Education, Inc. Publishing as Prentice Hall.
Martin-Gay, Prealgebra & Introductory Algebra, 3ed
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Perpendicular Lines
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
Copyright © 2011 Pearson Education, Inc. Publishing as Prentice Hall.
Martin-Gay, Prealgebra & Introductory Algebra, 3ed
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Vertical Angles
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
ma = m c
md = mb
Copyright © 2011 Pearson Education, Inc. Publishing as Prentice Hall.
Martin-Gay, Prealgebra & Introductory Algebra, 3ed
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Adjacent Angles
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
Copyright © 2011 Pearson Education, Inc. Publishing as Prentice Hall.
Martin-Gay, Prealgebra & Introductory Algebra, 3ed
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Transversal Lines
A line that intersects two or more lines at different
points is called a transversal.
Copyright © 2011 Pearson Education, Inc. Publishing as Prentice Hall.
Martin-Gay, Prealgebra & Introductory Algebra, 3ed
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Parallel Lines Cut by a Transversal
If two parallel lines are cut by a transversal,
then the measures of corresponding angles
are equal and the measures of the alternate
interior angles are equal.
a b
c d
e f
g h
Copyright © 2011 Pearson Education, Inc. Publishing as Prentice Hall.
Martin-Gay, Prealgebra & Introductory Algebra, 3ed
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Corresponding angles
Corresponding angles have equal measures.
a
b
d
c
f
e
g
h
ma = me
mc = mg
mb = mf
md = mh
Copyright © 2011 Pearson Education, Inc. Publishing as Prentice Hall.
Martin-Gay, Prealgebra & Introductory Algebra, 3ed
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Alternate Interior Angles
Alternate interior angles are angles on opposite
sides of the transversal between the two parallel
lines.
a
b
c
f
e
g
d
h
mc = m f
md = me
Copyright © 2011 Pearson Education, Inc. Publishing as Prentice Hall.
Martin-Gay, Prealgebra & Introductory Algebra, 3ed
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