Download Section 9.1 Points, Lines, Planes, and Angles

Section 9.1
Points, Lines,
Planes, and
Angles
Copyright 2013, 2010, 2007, Pearson, Education, Inc.
INB Table of Contents
2.3-2
Date
Topic
May 19, 2014
Test #1 Practice Test
14
May 19, 2014
Test #1 Practice Test Workspace
15
May 19, 2014
Section 9.1 Examples/Foldable
16
May 19, 2014
Section 9.1 Notes
17
May 19, 2014
Section 9.2 Examples
18
May 19, 2014
Section 9.2 Notes
19
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Page #
What You Will Learn

Points

Lines

Planes

Angles
9.1-3
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Basic Terms
Description
Diagram
Line AB
A
Ray AB
B
B
A
Line segment AB
A
AB
AB
B
A
Ray BA
9.1-4
Symbol
B
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BA
AB
Plane
We can think of a plane as a twodimensional surface that extends infinitely in
both directions.
Any three points that are not on the same
line (noncollinear points) determine a unique
plane.
9.1-5
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Plane
Two lines in the same plane that do
not intersect are called parallel lines.
9.1-6
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Angles
An angle is the union of two rays with a
common endpoint; denoted .
9.1-7
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Angles

The vertex is the point common to both
rays.
 The sides are the rays that make the
angle.
 There are several ways to name an angle:
ABC, CBA, B
9.1-8
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Angles
9.1-9
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Types of Angles

Adjacent Angles - angles that have a common
vertex and a common side but no common
interior points.

Complementary Angles - two angles whose
sum of their measures is 90 degrees.

Supplementary Angles - two angles whose
sum of their measures is 180 degrees.
9.1-10
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Example 3: Determining Complementary
Angles
In the figure, we see that ABC = 28
ABC & CBD are complementary angles.
Determine mCBD.
9.1-11
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Example 3: Determining Supplementary
Angles
In the figure, we see that ABC = 28.
ABC & CBE are supplementary angles.
Determine mCBE.
9.1-13
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Definitions
9.1-15

When two straight lines intersect, the
nonadjacent angles formed are called
Vertical angles.

Vertical angles have the same measure.
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Special Names
9.1-16
Alternate
interior angles
3 & 6; 4 & 5
Interior angles on
the opposite side of
the transversal–have
the same measure
Alternate
exterior angles
1 & 8; 2 & 7
Exterior angles on
the opposite sides of
the transversal–have
the same measure
Corresponding
angles
1 & 5, 2 & 6,
3 & 7, 4 & 8
One interior and one
exterior angle on the
same side of the
transversal–have the
same measure
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1
2
3
4
5 6
7 8
1
3
2
4
5 6
7 8
1
3
5 6
7 8
2
4
Example 6: Determining Angle
Measures
The figure
shows two
parallel lines
cut by a
transversal.
Determine the
measure of 1
through 7.
9.1-17
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Section 9.2
Polygons
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What You Will Learn

Polygons

Similar Figures

Congruent Figures
9.2-21
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Polygons
A polygon is a closed figure in a plane
determined by three or more straight
line segments.
9.2-22
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Polygons
Polygons are named according to
their number of sides.
9.2-23
Number
of Sides
Name
Number of
Sides
Name
3
Triangle
8
Octagon
4
Quadrilateral
9
Nonagon
5
Pentagon
10
Decagon
6
Hexagon
12
Dodecagon
7
Heptagon
20
Icosagon
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Polygons
Sides Triangles Sum of the Measures of
the Interior Angles
3
1
1(180º) = 180º
4
2
2(180º) = 360º
5
3
3(180º) = 540º
6
4
4(180º) = 720º
The sum of the measures of the
interior angles of an n-sided polygon
is (n – 2)180º.
9.2-24
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Example 3: Using Similar Triangles
to Find the Height of a Tree
Monique Currie plans to remove a tree
from her backyard. She needs to know
the height of the tree. Monique is 6 ft
tall and determines that when her
shadow is 9 ft long, the shadow of the
tree is 45 ft long (see Figure). How tall
is the tree?
9.2-25
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Example 3: Using Similar Triangles
to Find the Height of a Tree
9.2-26
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Example 3: Using Similar Triangles
to Find the Height of a Tree
9.2-27
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Congruent Figures

If corresponding sides of two similar
figures are the same length, the figures
are congruent.

Corresponding angles of congruent
figures have the same measure.
9.2-29
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Quadrilaterals

Quadrilaterals are four-sided polygons,
the sum of whose interior angles is 360º.

Quadrilaterals may be classified
according to their characteristics.
9.2-30
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Example 5: Angles of a Trapezoid
Trapezoid ABCD is shown.
a) Determine the measure of the interior
angle, x.
b) Determine the measure of the exterior
angle, y.
9.2-31
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Example 5: Angles of a Trapezoid
9.2-32
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