Unit 1 concept 3 angles and their measurements
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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

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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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Unit 1 concept 3 angles and their measurements

  • Find the measure of BOD

D

C

A

B

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Unit 1 concept 3 angles and their measurements

  • Find the measure of AOD

D

C

A

B

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Unit 1 concept 3 angles and their measurements

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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Unit 1 concept 3 angles and their measurements

  • Classify each angle AOY

  • as right, acute, obtuse or straight.

Y

X

Z

A

B

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Unit 1 concept 3 angles and their measurements

  • Classify each angle BOY

  • as right, acute, obtuse or straight.

Y

X

Z

A

B

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Unit 1 concept 3 angles and their measurements

  • Classify each angle BOA

  • as right, acute, obtuse or straight.

Y

X

Z

A

B

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Unit 1 concept 3 angles and their measurements

  • 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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Unit 1 concept 3 angles and their measurements

What can you deduce from this diagram?

  • A D

  • B E

  • C

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Unit 1 concept 3 angles and their measurements

What can you deduce from this diagram?

  • A D

  • B E

  • C

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Unit 1 concept 3 angles and their measurements

  • 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?

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