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Warm UpTopic: Segment Bisectors Draw Both

In the diagram above, Y is the midpoint. 𝑋𝑌 = 4𝑥 + 2 𝑎𝑛𝑑 𝑋𝑍 = 28

𝑋𝑌 =

𝑋𝑍 = 𝑌𝑍 =

𝑥 =

In the diagram above 𝐴𝐵 = 2𝑥 − 2,𝐵𝐶 = 𝑥 + 9 𝑎𝑛𝑑 𝐴𝐶= 4x - 1

𝐴𝐵 =

𝐵𝐶 = 𝐴𝐶 =

𝑥 =

HW: pg.15 #5-18all

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HW: pg.16 #33-40 all

Warm-Up Part 2With a partner brainstorm everything you know about angles

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Today’s Agenda

▪ Learning Targets:– I can name angles and find their measures

– I can state and use the angle addition postulate

▪ Brainstorm Activity

▪ Notes: Section 1-4

▪ Classwork

▪ Homework

Section 1-4: Angles

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Angle

▪ The figure formed by two rays that have the same endpoint

▪ Rays: sides 𝐵𝐴 𝑎𝑛𝑑 𝐵𝐶– Common endpoint = vertex B

– Notation: ∠ 𝑜𝑟 ∡

A

B C

Naming Angles

▪ Need three letters or a number

B

Q D

C

1

2

With #: ∡ 1 , ∡ 2

With 3 Letters: ∡BQC , ∡DQC• The angle must go in the

middle

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Measuring Angles

▪ Degree: the unit for measuring angles

▪ 58°

▪ Postulate 3: Protractor Postulate–Gives a method/system for measuring

angles

Symbol

Classification for Angles

Acute

▪ Definition: between 0°and 90°

▪ Examples:

Create your own example

15 °

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Classification for Angles

Obtuse

▪ Definition: between 90°and 180°

▪ Examples:

Create your own example

165 °110 °

Classification for Angles

Right

▪ Definition: exactly 90°

▪ Examples:

⊓

Means right ∡

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Classification for Angles

Straight

▪ Definition: exactly 180°

▪ Examples:

Straight line

Postulate 4: Angle Addition Postulate

1.If point B lies in the interior of ∠𝐴𝑂𝐶, then

m ∠𝐴𝑂𝐵 +𝑚∠𝐵𝑂𝐶 = 𝑚∠𝐴𝑂𝐶

A

OC

B

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Postulate 4: Angle Addition Postulate

2. If ∠𝐴𝑂𝐶 is a straight line and B is any point not on 𝐴𝐶, then

m ∠𝐴𝑂𝐵 +𝑚∠𝐵𝑂𝐶 = 180

AO

C

B

Example 1

B

Q D

C

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Example 2 Calculate x

(4x+3)°(6x+7)°

Congruent Angles

▪ Angles that have the same measures

40

R

40

S

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Adjacent Angles

▪ Two angles in a plane that have a –Common endpoint (vertex)

–Common side

–But no common interior points (no overlap)

Bisector of an angle

▪ The ray that divides the angle into two congruent adjacent angles

A

BC

d𝐵𝑑 𝑏𝑖𝑠𝑒𝑐𝑡𝑠 ∠𝐴𝐵𝐶𝐵𝑑 is the bisector of ∠𝐴𝐵𝐶∠𝐴𝐵𝐶 is bisected by 𝐵𝑑

∠𝑨𝑩𝒅 ≅ ∠𝒅𝑩𝑪

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Example 1

Example 2

A

BC

B

8x-12

5x+9

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Find your partner below and sit together. Bring your book, paper and a calculator

Lauren & Madison

Shannon & Ryleigh

Kim & Chris A

Julia A & Gabriella

Sam B. & Clayton

Chris G. & Carolyn Nikita & Emily

Matt & Sam M. Jeremy & Erica

Ryan M & Ethan H.

James & Julia R.

Gary & MacKenzie

Gianna & Ethan A.

Dalton & Devon

Partner Practice Directions

▪ With your partner, you will both complete pg. 20 #1-16

▪ When you are finished, you will both bring your papers to me to check your work

▪ If there is extra time, begin working on the crossword puzzle

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Closure: You are the teacher

▪ I would like you to create two quiz questions and include their answers

▪ These questions must be from the material from today’s lesson

▪ You will email these two questions to mwasser@cbsd.org

▪ Please label the subject of the email as quizquestions_lastname_block #

▪ I will include some of these questions in the warm-up on Monday

Homework

▪ Complete pg. 21 #3-18 & pg. 22 #29-30

▪ Selfieometry picture/caption due Monday

▪ Quiz Monday–Section 1-2, 1-5, 1-3

▪ Test Wednesday