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IM 8 Ch 9.1.3 What If The Angle Is On The Outside

CPM Materials modified by Mr. Deyo

How are the angles related?

Can I make a triangle?

What if it is a right angle?

What do I know about this triangle?

Common Core Standard: 8.G.5


By the end of the period, I will calculate and verify that the exterior angle of a triangle is equal to the sum of the two remote angles.

I will demonstrate this by completing Four‑Square notes and by solving problems in a pair/group activity.

Learning TargetTitle: IM8 ‑ Ch. 9.1.3 What If The Angle Is On The Outside? Date:


Home Work: Sec. 9.1.3Desc. Date Due

Review & Preview

3 Problems 9‑33, 9‑34, 9‑35



Vocabulary1) Exterior Angle

2) Remote Interior Angles

3) Exterior Angles Theorem

4) Triangle Sum Theorem



9.1.3 What If The Angle Is On The Outside?So far in this section, you have investigated angle relationships in situations with parallel lines and within triangles. In this lesson, you will continue to look at angle relationships. This time, you will investigate the angle relationships on the inside and outside of a triangle.

927. Use the diagram at right to name each of the indicated angles below using three letters. Reread the Math Notes box in Lesson 9.1.1 if you need to remember how to do this.

a) a =

b) b =

c) c =

___ ___ ___

___ ___ ___

___ ___ ___


928. Read the information below. Then follow the directions that follow.

Exterior angles are formed by extending a side of the triangle. The two angles across the triangle from the exterior angle are called remote interior angles. In each figure located below part (a), A and B are remote interior angles with respect to exterior angle BCD.

These are exterior angles: These are NOT exterior angles:


928 (continued) a) Calculate the missing angle measures in each figure and record them in the table. When you have completed the resource page, look for a pattern in the relationship between the measure of BCD (the exterior angle) and the sum of the measures of A and B (the remote interior angles). (Note that m BCD means the measure of BCD. Similarly, m A means the measure of A.)

http://www.cpm.org/pdfs/stuRes/CC3/chapter_09/CC3%20Lesson%209.1.3%20RP.pdf



928 (continued) b) Compare your results for m BCD (the exterior angle) and the sum of m A and m B (the remote interior angles) for each figure. Discuss your observations with your team.

c) Write a conjecture about the relationship of an exterior angle to the two remote interior angles.




929. Calculate the measures of the angles requested. Each part is a separate problem.

a) If m 1 = 53° and m 2 = 71°, find m 4.

b) If m 2 = 78° and m 4 = 127°, find m 1.


930a,b. Use your conjecture from part (c) of problem 928 to solve for x in each figure below.

a) b)


930c,d. Use your conjecture from part (c) of problem 928 to solve for x in each figure below.

c) *d)

2x


931. Additional Challenge: Solve for x in the figure below.


932. LEARNING LOG "Angle Relationships Pt. 2" Date _______Look back at the entry that you created in Lesson 9.1.1 (“Angle Relationships”). Add to that entry the angle relationships that you learned in this lesson. Use appropriate geometry vocabulary and include diagrams.


933. Based on the given information, determine which pairs of lines, if any, are parallel. If none are necessarily parallel, write “none.”

a) m 2 = m 7

http://homework.cpm.org/cpmhomework/homework/category/CC/textbook/CC3/chapter/Ch9/lesson/9.1.3/problem/933

b)m 3 = m 11

c) m 1 = m 12

d)m 13 = m 12

e) 6 and 7 are supplementary.

http://homework.cpm.org/cpm-homework/homework/category/CC/textbook/CC3/chapter/Ch9/lesson/9.1.3/problem/9-33


934a. In the angle problem below, solve for the variable(s). Write the names of the definition(s) and relationship(s) that justify the steps in your solution.

a)


Reasons



934b. In the angle problem below, solve for the variable(s). Write the names of the definition(s) and relationship(s) that justify the steps in your solution.

b)


Reasons



934c. In the angle problem below, solve for the variable(s). Write the names of the definition(s) and relationship(s) that justify the steps in your solution.

c)


Reasons



935a,b. Simplify each expression.

a) 54

b)


7 16

1013

5 11.



935c,d. Simplify each expression.

c) 9 11

d)


2021

83

5 18

( ) ( )



936a,b. Simplify and solve each equation below for x. Show your work and check your answer.

24 = 3x + 3a) b)

2(x − 6) = x − 14




936c,d. Simplify and solve each equation below for x. Show your work and check your answer.

3(2x − 3) = 4x − 5c) d)

x = 2x − 5


34



937. Joaquin has agreed to lend his younger brother $45 so that he can buy a new tank for his pet lizard.

a) Joaquin is charging his brother 2% simple interest per month. If his brother pays him back in 6 months, how much will Joaquin get back?

b) If Joaquin’s brother instead borrowed the money from a bank at 2% compound interest per month, how much would he have to pay the bank at the end of 6 months?

Joaquin will get $ _______ . ____ back from his brother.


Joaquin's brother would have to pay $ _______ . ____ to the bank.



938a. Martha is saving money to buy a new laptop computer that costs $1800. She received $200 for her birthday and has a job where she makes $150 each week. a) Make a table and a graph for this situation.Wk $$

01234567

Wk $$

89101112131415

https://www.desmos.com/calculator/45uxximqwv http://homework.cpm.org/cpmhomework/homework/category/CC/textbook/CC3/chapter/Ch9/lesson/9.1.3/problem/938

1,000

2,000

5 10

https://www.desmos.com/calculator/45uxximqwv



938b,c. Martha is saving money to buy a new laptop computer that costs $1800. She received $200 for her birthday and has a job where she makes $150 each week. https://www.desmos.com/calculator/45uxximqwv http://homework.cpm.org/cpmhomework/homework/category/CC/textbook/CC3/

chapter/Ch9/lesson/9.1.3/problem/938

b) Explain how you can use the table or graph to predict how many weeks it will take Martha to earn enough money to pay for the new computer.

c) Explain how you can tell from both the table and the graph whether this is an example of linear or nonlinear growth.

https://www.desmos.com/calculator/45uxximqwv


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Can I make a triangle? What if it is a right angle?helpmeteach.weebly.com/uploads/1/7/1/0/17102056/im_8__ch_9.1.3... · Can I make a triangle? What if it is a ... Reread the Math