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
IM 8 Ch 9.1.3 What If The Angle Is On The Outside
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:
IM 8 Ch 9.1.3 What If The Angle Is On The Outside
Home Work: Sec. 9.1.3Desc. Date Due
Review & Preview
3 Problems 9‑33, 9‑34, 9‑35
IM 8 Ch 9.1.3 What If The Angle Is On The Outside
Vocabulary1) Exterior Angle
2) Remote Interior Angles
3) Exterior Angles Theorem
4) Triangle Sum Theorem
IM 8 Ch 9.1.3 What If The Angle Is On The Outside
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 =
___ ___ ___
___ ___ ___
___ ___ ___
IM 8 Ch 9.1.3 What If The Angle Is On The Outside
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:
IM 8 Ch 9.1.3 What If The Angle Is On The Outside
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
IM 8 Ch 9.1.3 What If The Angle Is On The Outside
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.
http://www.cpm.org/pdfs/stuRes/CC3/chapter_09/CC3%20Lesson%209.1.3%20RP.pdf
IM 8 Ch 9.1.3 What If The Angle Is On The Outside
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.
IM 8 Ch 9.1.3 What If The Angle Is On The Outside
930a,b. Use your conjecture from part (c) of problem 928 to solve for x in each figure below.
a) b)
IM 8 Ch 9.1.3 What If The Angle Is On The Outside
930c,d. Use your conjecture from part (c) of problem 928 to solve for x in each figure below.
c) *d)
2x
IM 8 Ch 9.1.3 What If The Angle Is On The Outside
931. Additional Challenge: Solve for x in the figure below.
IM 8 Ch 9.1.3 What If The Angle Is On The Outside
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.
IM 8 Ch 9.1.3 What If The Angle Is On The Outside
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.
IM 8 Ch 9.1.3 What If The Angle Is On The Outside
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)
http://homework.cpm.org/cpmhomework/homework/category/CC/textbook/CC3/chapter/Ch9/lesson/9.1.3/problem/934
Reasons
IM 8 Ch 9.1.3 What If The Angle Is On The Outside
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)
http://homework.cpm.org/cpmhomework/homework/category/CC/textbook/CC3/chapter/Ch9/lesson/9.1.3/problem/934
Reasons
IM 8 Ch 9.1.3 What If The Angle Is On The Outside
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)
http://homework.cpm.org/cpmhomework/homework/category/CC/textbook/CC3/chapter/Ch9/lesson/9.1.3/problem/934
Reasons
IM 8 Ch 9.1.3 What If The Angle Is On The Outside
935a,b. Simplify each expression.
a) 54
b)
http://homework.cpm.org/cpmhomework/homework/category/CC/textbook/CC3/chapter/Ch9/lesson/9.1.3/problem/935
7 16
1013
5 11.
IM 8 Ch 9.1.3 What If The Angle Is On The Outside
935c,d. Simplify each expression.
c) 9 11
d)
http://homework.cpm.org/cpmhomework/homework/category/CC/textbook/CC3/chapter/Ch9/lesson/9.1.3/problem/935
2021
83
5 18
( ) ( )
IM 8 Ch 9.1.3 What If The Angle Is On The Outside
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
http://homework.cpm.org/cpmhomework/homework/category/CC/textbook/CC3/chapter/Ch9/lesson/9.1.3/problem/936
IM 8 Ch 9.1.3 What If The Angle Is On The Outside
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
http://homework.cpm.org/cpmhomework/homework/category/CC/textbook/CC3/chapter/Ch9/lesson/9.1.3/problem/936
34
IM 8 Ch 9.1.3 What If The Angle Is On The Outside
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.
http://homework.cpm.org/cpmhomework/homework/category/CC/textbook/CC3/chapter/Ch9/lesson/9.1.3/problem/937
Joaquin's brother would have to pay $ _______ . ____ to the bank.
IM 8 Ch 9.1.3 What If The Angle Is On The Outside
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
IM 8 Ch 9.1.3 What If The Angle Is On The Outside
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.