Geometry and Measurement

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Geometry and Measurement
Chapter Nine
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Lines and Angles
Section 9.1
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A plane is a flat surface that extends
indefinitely.
Plane
Space extends in all directions indefinitely.
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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
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A
B
A
B
A
B
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An angle is made up of two rays that share the
same endpoint called a vertex.
Vertex
The angle can be named ?ABC, ?CBA, ?B, or ?x.
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An angle can be measured in degrees. There are
360º (degrees) in a full revolution or full
circle.
360º
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Classifying Angles
Name
Angle Measure
Examples
Acute Angle
Between 0 and 90
Right Angle
Exactly 90
Obtuse Angle
Between 90 and 180
Straight Angle
Exactly 180º
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Two angles that have a sum of 90 are called
complementary angles.
Two angles that have a sum of 180 are called
supplementary angles.
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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.
Parallel lines
Intersecting lines
p ?? q
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Two lines are perpendicular if they form right
angles when they intersect. The symbol ? is
used to denote is perpendicular to.
Perpendicular lines
n ? m
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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.
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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 and ?b
?b and ?c
?c and ?d
?d and ?a
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A line that intersects two or more lines at
different points is called a transversal.
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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 alternate interior angles are equal.

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Corresponding angles are equal.
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Alternate interior angles are angles on opposite
sides of the transversal between the two parallel
lines.
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