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Unit #1, Concept #3 Angles and their Measurements. 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…

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unit 1 concept 3 angles and their measurements
Unit #1, Concept #3Angles and their Measurements
  • 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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bell ringer
Bell Ringer

With your partner…

Come up with a list of some things that you remember about angles.

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an angle
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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naming angles
Naming Angles
  • 1
  • Naming Angles

C

B

A

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postulate 1 7 protractor postulate
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|.

D

C

y

x

A

B

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slide6

Find the measure of BOD

D

C

A

B

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slide7

Find the measure of AOD

D

C

A

B

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slide8

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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slide9

Classify each angle AOY

  • as right, acute, obtuse or straight.

Y

X

Z

A

B

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slide10

Classify each angle BOY

  • as right, acute, obtuse or straight.

Y

X

Z

A

B

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slide11

Classify each angle BOA

  • as right, acute, obtuse or straight.

Y

X

Z

A

B

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slide12

Classify each angle XOZ

  • as right, acute, obtuse or straight.

Y

X

Z

A

B

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find the measure of the following aox xoy yoz xoz yob
Find the measure of the followingAOX, XOY, YOZ, XOZ, YOB

Y

X

Z

A

B

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let s get it started
Let’s Get it Started
  • What did the segment addition postulate state?

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postulate 1 8 angle addition postulate
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
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 postulate1
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 postulate2
Using the Angle Addition Postulate
  • Find the measure of angle 1

153°

1

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using the angle addition postulate3
Using the Angle Addition Postulate
  • Find the value of x.

(3x + 5)°

(9x + 7)°

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congruent angles
Congruent Angles
  • Are angles with the same measure.

1

2

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slide21

What can you deduce from this diagram?

  • A D
  • B E
  • C

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slide22

What can you deduce from this diagram?

  • A D
  • B E
  • C

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slide23

Journal Entry

  • 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
Classwork/Homework
  • Page 30 – 32
  • # 17 – 23 odd, 24 – 28 all, 47, 48, 56-67, 70, 75

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unit 1 concept 3 angles and their measurements1
Unit #1, Concept #3Angles and their Measurements
  • 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?

Free Template from www.brainybetty.com

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