Download Angle

Chapter 6
Geometry
Copyright © 2011 Pearson Education, Inc. Publishing as Prentice Hall.
6.1
Lines and Angles
Copyright © 2011 Pearson Education, Inc. Publishing as Prentice Hall.
Identifying Lines, Line Segments. Rays, and
Angles
Space extends in all directions indefinitely.
A Plane is a flat surface that extends indefinitely.
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Martin-Gay, Developmental Mathematics, 2e
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Identifying Lines, Line Segments. Rays, and
Angles
A point has no length, no width, and no height, but it does
have a location.
P
Point P
A line is set of points extending indefinitely in two
directions.
A
B
Line AB or AB
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Identifying Lines, Line Segments. Rays, and
Angles
Definition
Line Segment - A piece of a
line with two endpoints.
Ray - A part of a line with one
endpoint.
Angle - Made up of two rays
that share the same endpoint.
Vertex - The common
endpoint of an angle.
Example
A
B
Line segment AB or AB.
A
B
Ray AB or AB.
A
B
Vertex
C
ABC or CBA
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Example
Identify each figure as a line, a ray, a line segment, or an
angle. Then name the figure using the given point.
a.
b.
c.
This is a ray. It is ray FG or FG.
N
This is a line segment. It is line segment
NP or NP.
P
•
R
•
S
This is a line. It is line RS or RS .
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Classifying Angles as Acute, Right, Obtuse, or
Straight
Definition
Degrees - used to measure
angles, symbolized by a small
raised circle .
Straight angle - an angle that
measures 180.
Right angle - an angle that
measures 90.
Example
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Classifying Angles as Acute, Right, Obtuse, or
Straight
Definition
Acute Angle - an angle whose
measure is between 0 and
90.
Example
Obtuse angle - an angle that
measures between 90 and
180.
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Identifying Complementary and
Supplementary Angles
Definition
Complementary Angles –
two angles that have a sum
of 90.
Example
Supplementary Angles –
two angles that have a sum
of 180.
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Example
Find the complement of a 62 angle.
Two angles that have a sum of 90 are complementary.
90  62  28
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Example
Find the supplement of a 121 angle.
Two angles that have a sum of 180 are supplementary.
180  121  59
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Finding Measures of Angles
Two lines in a place can either be parallel or intersection.
Parallel lines never meet. The symbol‖is used to indicate
“parallel to”.
Perpendicular lines form right angles when they
intersect. The symbol  is used to denote perpendicular
lines.
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Vertical and Adjacent Angles
When two lines intersect, four angles are formed. Two
angles that are opposite each other are called vertical
angles. Vertical angles have the same measure. Two
angles that share a common side are called adjacent
angles. Adjacent angles formed by intersecting lines are
supplementary.
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Parallel Lines
Parallel Line Cut by a Transversal
If two parallel lines are cut by a transversal, then the
measure of corresponding angles are equal and the
measure of the alternate interior angles are equal.
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Example
m || n, find the measures of x, y, and z.
x  180  80  100
z  x  100
x
80°
y
z
y  180  100  80
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