How are the angles related? Can I make a triangle? What if it is a right angle? What do I know about this triangle? CPM Materials modified by Mr.
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1 Common Core Standard: 8.G.5 How are the angles related? Can I make a triangle? What if it is a right angle? What do I know about this triangle? CPM Materials modified by Mr. Deyo
2 Title: IM8 Ch How Can I Find A Missing Angle? Date: Learning Target By the end of the period, I will calculate and verify that the sum of the angles in any triangle is 180. I will demonstrate this by completing Four Square notes and by solving problems in a pair/group activity.
3 Home Work: Sec Desc. Date Due Review & Preview 3 Problems 9 21, 9 22, 9 23
4
5 Vocabulary 1) Acute Angle 2) Right Angle 3) Obtuse Angle 4) Exterior Angle 5) Sides
6
7 9.1.2 How Can I Find A Missing Angle? In today s lesson, you will be challenged again to use what you do know to determine information that you did not previously know, in order to solve problems with variables. You will do an investigation to learn a new geometric relationship for triangles Quigley was excited about what he had learned about angles. He went home, grabbed his older brother s math book, and tried to find some problems that he could do with angles. He came across the following problem that he wanted to solve. a) Using what you have learned about angles, can you find the measure of the angle? Solve for the value of x in the figure: Why or why not? b) Estimate the measure of the angle.
8 9 15. TANGLED TRIANGLES %20RP.pdf %20RP.pdf %20RP.pdf Your teacher will give your team a copy of the Lesson 9.1.2A, 9.1.2B, 9.1.2C, and 9.1.2D Resource Pages. Cut out the three copies of the triangle. Your Task: Determine the measure of the missing angle without using a protractor. As you work with your team, the following questions might help guide your discussion. What do we know about angles? %20RP.pdf Can we combine the unknown angle with any other angles to create a new angle that we do know? 9.1.2A 9.1.2B 9.1.2C 9.1.2D
9 9 15a. TANGLED TRIANGLES 9.1.2A %20RP.pdf Your Task: Determine the measure of the missing angle without using a protractor. As you work with your team, the following questions might help guide your discussion. What do we know about angles? Can we combine the unknown angle with any other angles to create a new angle that we do know? 90 y A 90 y 90 y C B
10 %20RP.pdf IM 8 Ch How Can I Find a Missing Angle 9 15b. TANGLED TRIANGLES 9.1.2B Your Task: Determine the measure of the missing angle without using a protractor. As you work with your team, the following questions might help guide your discussion. What do we know about angles? Can we combine the unknown angle with any other angles to create a new angle that we do know? w A w B w C
11 9 15c. TANGLED TRIANGLES 9.1.2C %20RP.pdf Your Task: Determine the measure of the missing angle without using a protractor. As you work with your team, the following questions might help guide your discussion. What do we know about angles? Can we combine the unknown angle with any other angles to create a new angle that we do know? z A z 55 B z C
12 9 15d. TANGLED TRIANGLES 9.1.2D %20RP.pdf Your Task: Determine the measure of the missing angle without using a protractor. As you work with your team, the following questions might help guide your discussion. What do we know about angles? Can we combine the unknown angle with any other angles to create a new angle that we do know? 80 A s B s C s 60
13 9 16. Be prepared to contribute what your team has discovered to a whole class discussion. Use the Triangle Sum Theorem (Desmos) to explore the sum of the angles in a triangle. Keep track of what each team has found to see if you can find a relationship that would allow you to find a missing angle in any triangle y z A A w A s A 60
14 9 17. Now use what you have discovered about the angles in a triangle to find the answer to the problem that Quigley was trying to solve in problem How close was your estimate?
15 9 18. Use what you have learned about triangles and angles to write an equation that represents each situation. Then find each of the missing angle(s) in the triangles below. a) b)
16 9 19a,b. Additional Challenge: Use what you know about triangles and angle relationships to find the missing angles in the triangles. a) b)
17 9 19c,d. Additional Challenge: Use what you know about triangles and angle relationships to find the missing angles in the triangles. c) d)
18 9 20. LEARNING LOG "Angles In A Triangle" Date Today you explored a fundamental concept about a triangle and the sum of its angles. In your Learning Log, state this relationship in your own words and include at least one example that shows how to use this idea.
19 9 21. Find the measure of the missing angle in each triangle below and then classify the triangle as acute, right, or obtuse. homework/h chapter/ch9/lesson/9.1.2/problem/9 21 a) b)
20 9 22. Find the measures of the angles requested and explain how you found them. Each part is a separate problem. homework/homework/category/cc/textbook/cc3/ chapter/ch9/lesson/9.1.2/problem/9 22 a) If m 4 = 61, find m 6. c) If m 2 = 137, find m 8. b) If m 1 = 48, find m 8.
21 9 23. Graph the rule y = 2x 6. Create a table if it will help. chapter/ch x y
22 9 24. On graph paper, graph the data in the table. Is there an association? homework/homework/category/cc/textbook/cc3/ chapter/ch9/lesson/9.1.2/problem/9 24
23 9 25. Tina s rectangular living room floor measures 15 feet by 18 feet. chapter/ch9/les a) How many square feet of carpet will Tina need to cover the entire floor? Tina will need square feet of carpet to cover the entire floor. b) The carpet Tina likes is sold by the square yard. How many square yards will she need? Tina will need square yards of carpet to cover the entire floor.
24 9 26. Solve for y in terms of x. That is, rewrite each equation so that it starts with y =. homework/h chapter/ch9/lesson/9.1.2/problem/9 26 a) 6x + 5y = 20 b) 4x 8y = 16 y = y =
25 9 13. Determine whether the graphs below are functions or not functions. hom chapter/ch9/lesson/9.1.1/problem/ Yes / No Yes / No Yes / No Yes / No Yes / No Yes / No Explain your reasoning.
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