Download - 3 Geometry Angles
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Tennessee Adult Education
GeometryLesson 3
This curriculum was written with funding of the Tennessee Department of Labor and Workforce Development and may not be reproduced in any way without written permission. ©
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What is Geometry?
•It is the branch of mathematics that deals with lines, points, curves, angles, surfaces, and solids.
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Term Definition
The following key terms are important to know when discussing angles.
(•)
Point
Line
Line Segment
Ray
A specific location on an object or a specific position in space.
A connected set of points that extends without end in two directions.
A piece of a line, like a jump rope.
Part of a line that extends indefinitely in one direction.
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Term Definition
Parallel Lines Lines that are always the same distance They will never intersect.
Perpendicular Lines
Lines that form a right angle when they intersect
Intersecting Lines Lines that cross, or that will cross. The point at which they cross is called the vertex.
Transversal Lines Lines that intersect a set of parallel lines.
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What are angles?
•An angle measures the amount of a turn.•As the Angle Increases, the Name Changes.
Pictures from clipart
Mr. Smiles fell at an angle of 90⁰. He fell at a right angle.
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Type of Angle Description
Acute An angle less than 90⁰
Right An angle that is exactly 90⁰
Obtuse An angle that is greater than 90⁰
Straight An angle that is exactly 180⁰
Reflex An angle that is greater than 180⁰
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Find the Angles!
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Walnut St. Bridge, Chattanooga
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Parallel Lines
Review!
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Right Angle
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Acute
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Obtuse Angle
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Straight Angle
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Perpendicular Lines
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Parts of an AngleR
ay
Ray
·angle
Vertex
•The two straight sides are called rays.
• The point at which the two rays meet is called the vertex.
•The angle is the amount of a turn between each ray.
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Naming Angles•There are two main ways to name angles:
1) Name an angle by the vertex.
For example: B is the point at which both rays intersect.
2) Name an angle by all three letters.
For example: A B C or C B A
HINT: The vertex is always the middle letter
A
B
C
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Guided practice
•Directions: Name and classify the following angles. (Provide 3 ways to name each angle.) 1. 2.
3.4.
A
B C
C
E
F
G HKJ
I
DReflex Angle B ABC CBA
Acute Angle D CDE EDC
Obtuse Angle G FGH HGF
Right Angle J IJK KJI
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Supplementary AnglesThe two angles below (140⁰ + 40⁰) are supplementary angles, because their measurements add up to 180⁰.
NOTICE: When the two angles are put together, they form a straight line.
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Supplementary Angles
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Supplementary cont.
But, the angles don't have to be together.These two are supplementary because:
60° + 120° = 180°
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Complementary Angles
•The two angles at the right (40° + 50°) are Complementary Angles, because they add up to 90°.
•NOTICE: When the two angles are placed together, they form a corner.
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Complementary cont.•But, the angles don't have to be together.•These two are complementary because their measurements add up to 90⁰.•
• 27° + 63° = 90°
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Complementary Angles
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Complementary vs Supplementary
How can you remember which is which? Easy! Think:
• "C" of Complementary stands for "Corner" (a Right Angle), and
• "S" of Supplementary stands for "Straight" (180 degrees is a straight line)
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Find the missing angle using complementary or supplementary angles.
80
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Find the missing angle using complementary or supplementary angles.
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Find the missing angle using complementary or supplementary angles.
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Find the missing angle using complementary or supplementary angles.
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A
B
C
D
EF
<AFB and <BFC are complementary angles. If m<AFB = 50 ⁰, which expression could be used to find the measure of <BFC?
1. 180⁰ - 50 ⁰ 2. 90 ⁰ + 50 ⁰ 3. 180 / 50 ⁰ 4. 90 ⁰ (50 ⁰ )
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Guided Practice1. The train crosses Sesame Street and Big Bird Avenue at
an angle of 60⁰. What is the measure of the supplementary angle?
Sesame St.
Big Bird Ave.HINT: a line equals 180⁰. 180 - 60 = 120⁰ ⁰ ⁰
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2. Jo Jo is building a fence. In order to make it stronger, she will need to use a brace from one side to the ground. If the brace makes a 45⁰ angle with the fence what is the measure of the supplementary angle?
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A transversal line is a line that cuts through a set of parallel lines.
As the transversal cuts through, it forms both Corresponding and Vertical Angles
Angles Formed by A Transversal
Transversal line
AB CD
Corresponding angles have equal measurements, and vertical angles have equal measurements.
This reads as Line AB is parallel to Line CD.
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Corresponding Angles
The angles that occupy the same relative position at each intersection.
Therefore, the angles will have the same measurement.
2 & 6
The following angles are corresponding angles.
3 & 7
8&4
1 & 5
Example: If 3 is 130 , ⁰then 7 is also 130 . ⁰
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Vertical Angles
E
BA
C D
F
2 1
3 4
56
7 8
Vertical angles are angles that are opposite from each other.
For example: 2 & 4 are vertical, because they are diagonal from each other.
Therefore, if 2 equals 50⁰, then 4 is also 50⁰.
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Guided Practice
E
BA
C D
F
Directions: Fill in the missing angles if angle 1 equals 75⁰
2
6
Identify the vertical angles.
1. ________________
2. ________________
3. ________________
4. ________________
Identify the corresponding angles.
1. _________________
2. _________________
3. _________________
4. _________________
43
1
7 8
5
1
3
51
32
4
7
85
6 7
84
62
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If the lines are parallel and m<2 is 45⁰ in the figure above, what is the measure of <3?
1. 30 ⁰ 2. 45 ⁰ 3. 90 ⁰ 4. 135 ⁰ 5. 180 ⁰
1
5 6
2 3 4
7 8
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Vertical Angles vs. Corresponding
*Vertical angles are always equal. However, you can not assume you have corresponding angles unless dealing with a transversal.
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Triangles
A triangle has three sides and three angles
The three angles always add up to 180°
a
b c
a + b + c = 180⁰
Why do I need to know about triangles?
The GED Test will ask testers to identify missing angles. In order to answer those questions, a person must have an understanding of triangles and their characteristics.
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Equilateral, Isosceles and Scalene
There are three special names given to triangles that tell how many sides are equal.
Equilateral Triangle Three equal sides
Three equal angles, always 60°
Isosceles Triangle Two equal sides
Two equal angles
Scalene Triangle No equal sides
No equal angles
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70
55
Find the missing angle measurement.
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5050
Find the missing angle measurement.
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6085
Find the missing angle measurement.