unit #1, concept #3 angles and their measurements
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Unit #1, Concept #3Angles and their Measurements
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• What are angles and how are they classified?
• How are the measures of angles used to determine their congruency?
• What is angle addition and how is it used?
Bell Ringer
With your partner…
Come up with a list of some things that you remember about angles.
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An angle ( )
• Is formed by two rays with the same endpoint.
• The two rays are the sides of the angles. The endpoint is called the vertex of the angle
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1
• Naming Angles
B
A
C
Naming Angles
1,, BABC
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Postulate 1 – 7Protractor Postulate
• OA is paired with 0 and OB is paired with 180.
• If OC is paired with x and OD is paired with y, then m<COD = |x – y|.
A B
CD
x y
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A B
CD
• Find the measure of BOD
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A B
CD
• Find the measure of AOD
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Types of Angles
• Acute angles - an angle whose measure is between 0º and 90º.
• Right angle - an angle whose measure is 90º.
• Obtuse angle - an angle whose measure is between 90º and 180º.
• Straight angle - an angle whose measure is 180º
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A B
X
Z
• Classify each angle AOY
as right, acute, obtuse or straight.
Y
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A B
X
Z
• Classify each angle BOY
as right, acute, obtuse or straight.
Y
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A B
X
Z
• Classify each angle BOA
as right, acute, obtuse or straight.
Y
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A B
X
Z
• Classify each angle XOZ
as right, acute, obtuse or straight.
Y
Find the measure of the followingAOX, XOY, YOZ, XOZ, YOB
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B
X
Z
Y
A
Let’s Get it Started
• What did the segment addition postulate state?
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Postulate 1 – 8 Angle Addition Postulate
• If point B lies in the interior of AOC, then
• m AOB + m BOC = m AOC.
• C
• B
• O
• A
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Using the Angle Addition Postulate
• m AOB = 54
• m AOC = 76 Find m BOC.
C
B
O
A
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Using the Angle Addition Postulate
• m COB = 2x + 6
• m AOB = 5x – 11 and m AOC =79
C
B
O find x
A
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Using the Angle Addition Postulate
• Find the measure of angle 1
1 153°
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Using the Angle Addition Postulate
• Find the value of x.
(9x + 7)°(3x + 5)°
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Congruent Angles
• Are angles with the same measure.
21
21
or
mm
1
2
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What can you deduce from this diagram?
A D
B E
• C
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What can you deduce from this diagram?
A D
B E
• C
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Journal Entry
1.What are angles and how are they classified?
2. How are the measures of angles used to determine their congruency?
3. What is angle addition and how is it used?
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Classwork/Homework
• Page 30 – 32
• # 17 – 23 odd, 24 – 28 all, 47, 48, 56-67, 70, 75
Unit #1, Concept #3Angles and their Measurements
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• What are angles and how are they classified?
• How are the measures of angles used to determine their congruency?
• What is angle addition and how is it used?
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