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MM-150 SURVEY OF MATHEMATICS – Jody Harris
Unit 6
Geometry
Copyright © 2009 Pearson Education, Inc.
Slide 9 - 1
Basic Terms
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Slide 9 - 2
Angles




An angle is the union of two rays with a
common endpoint; denoted
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:
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Slide 9 - 3
Angles


The measure of an angle is the amount of
rotation from its initial to its terminal side.
Angles are classified by their degree
measurement.
 Right Angle is 90o
o
 Acute Angle is less than 90
 Obtuse Angle is greater than 90o but less
than 180o
o
 Straight Angle is 180
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Slide 9 - 4
Types of Angles
____ Straight Angle
____ Right Angle
____ Obtuse Angle
____ Acute Angle
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Slide 9 - 5
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.

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Slide 9 - 6
Example

If  ABC and CBD are supplementary and the
measure of ABC is 4 times larger than CBD,
determine the measure of each angle.
C
A
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B
D
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Example

If  ABC and CBD are supplementary and the
measure of ABC is 4 times larger than CBD,
determine the measure of each angle.
 ABC + CBD = 180
C
A
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B
D
Slide 9 - 8
Example

If  ABC and CBD are supplementary and the
measure of ABC is 4 times larger than CBD,
determine the measure of each angle.
 ABC + CBD = 180
C
x
A
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B
D
Slide 9 - 9
Example

If  ABC and CBD are supplementary and the
measure of ABC is 4 times larger than CBD,
determine the measure of each angle.
 ABC + CBD = 180
C
4x x
A
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B
D
Slide 9 - 10
Example

If  ABC and CBD are supplementary and the
measure of ABC is 4 times larger than CBD,
determine the measure of each angle.
 ABC + CBD = 180
C
4x x
A
Copyright © 2009 Pearson Education, Inc.
B
D
Slide 9 - 11
Example

If  ABC and CBD are supplementary and the
measure of ABC is 4 times larger than CBD,
determine the measure of each angle.
 ABC + CBD = 180
4x + x = 180
C
4x x
A
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B
D
Slide 9 - 12
Example

If  ABC and CBD are supplementary and the
measure of ABC is 4 times larger than CBD,
determine the measure of each angle.
 ABC + CBD = 180
4x + x = 180
5x = 180
Copyright © 2009 Pearson Education, Inc.
C
4x x
A
B
D
Slide 9 - 13
Example

If  ABC and CBD are supplementary and the
measure of ABC is 4 times larger than CBD,
determine the measure of each angle.
 ABC + CBD = 180
4x + x = 180
5x = 180
x = 36
Copyright © 2009 Pearson Education, Inc.
C
4x x
A
B
D
Slide 9 - 14
Example

If  ABC and CBD are supplementary and the
measure of ABC is 4 times larger than CBD,
determine the measure of each angle.
 ABC + CBD = 180
4x + x = 180
5x = 180
x = 36
C
4x x
A
B
D
 ABC = 4x = 4(36) = 144
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Slide 9 - 15
Example
Find x. Assume that angle 1 and angle 2
are complementary angles.
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Slide 9 - 16
Example
Find x. Assume that angle 1 and angle 2
are complementary angles.
x + 5x + 3 = 90
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Slide 9 - 17
Example
Find x. Assume that angle 1 and angle 2
are complementary angles.
x + 5x + 3 = 90
6x + 3 = 90
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Slide 9 - 18
Example
Find x. Assume that angle 1 and angle 2
are complementary angles.
x + 5x + 3 = 90
6x + 3 = 90
6x = 87
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Slide 9 - 19
Example
Find x. Assume that angle 1 and angle 2
are complementary angles.
x + 5x + 3 = 90
6x + 3 = 90
6x = 87
x = 14.5
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Slide 9 - 20
More definitions




Vertical angles are the nonadjacent angles
formed by two intersecting straight lines.
Vertical angles have the same measure.
A line that intersects two different lines, at two
different points is called a transversal.
Special angles are given to the angles formed
by a transversal crossing two parallel lines.
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Slide 9 - 21
Special Names
Interior angles on the
Alternate
interior angles opposite side of the
transversal–have the
same measure
Exterior angles on
Alternate
the opposite sides of
exterior
the transversal–have
angles
the same measure
Corresponding One interior and one
exterior angle on the
angles
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
2
4
5 6
7 8
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Types of Triangles
Acute Triangle
All angles are acute.
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Obtuse Triangle
One angle is obtuse.
Slide 9 - 23
Types of Triangles continued
Right Triangle
One angle is a right
angle.
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Isosceles Triangle
Two equal sides.
Two equal angles.
Slide 9 - 24
Types of Triangles continued
Equilateral Triangle
Three equal sides.
Three equal angles
(60º) each.
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Scalene Triangle
No two sides are
equal in length.
Slide 9 - 25
Similar Figures

Two polygons are similar if their corresponding
angles have the same measure and the lengths
of their corresponding sides are in proportion.
9
6
4
4
3
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6
6
4.5
Slide 9 - 26
Similar Figures

Two polygons are similar if their corresponding
angles have the same measure and the lengths
of their corresponding sides are in proportion.
9
6
4
4
3
6
6
4.5
Put brown inside green
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Slide 9 - 27
Example

Catherine Johnson wants to measure the height of
a lighthouse. Catherine is 5 feet tall and determines
that when her shadow is 12 feet long, the shadow
of the lighthouse is 75 feet long. How tall is the
lighthouse?
x
5
75
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12
Slide 9 - 28
Quadrilaterals


Quadrilaterals are four-sided polygons, the sum
of whose interior angles is 360o.
Quadrilaterals may be classified according to
their characteristics.
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Slide 9 - 29
Classifications

Trapezoid
Two sides are parallel.
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
Parallelogram
Both pairs of opposite
sides are parallel.
Both pairs of opposite
sides are equal in
length.
Slide 9 - 30
Classifications continued

Rhombus
Both pairs of opposite
sides are parallel.
The four sides are
equal in length.
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
Rectangle
Both pairs of opposite
sides are parallel.
Both pairs of opposite
sides are equal in
length. The angles
are right angles.
Slide 9 - 31
Classifications continued

Square
Both pairs of opposite
sides are parallel.
The four sides are
equal in length. The
angles are right
angles.
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Slide 9 - 32
Formulas
Figure
Rectangle
Square
Parallelogram
Triangle
Trapezoid
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Perimeter
Area
P = 2l + 2w
A = lw
P = 4s
A = s2
P = 2b + 2w
A = bh
P = s1 + s2 + s3
A  21 bh
P = s1 + s2 + b1 + b2 A  21 h(b1  b2 )
Slide 9 - 33