Transcript
Angles and Triangles
ACTIVITY 22
Triangle Trivia Lesson 22-1 Properties of Triangles and Side Lengths My Notes
Learning Targets: Determine when three side lengths form a triangle. Use the Triangle Inequality Property. Classify triangles by side length.
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SUGGESTED LEARNING STRATEGIES: Interactive Word Wall, Summarizing, Look for a Pattern, Graphic Organizer Students in Mr. Mira’s math class made up some geometry games. Here are the rules for the game Matt and Allie created. Triangle Trivia Rules Properties of Triangles—Perimeter Variation Players: Materials:
Directions:
Three to four students Three number cubes and a “segment pieces” set of three each of the following lengths: 1 inch, 2 inches, 3 inches, 4 inches, 5 inches, and 6 inches. Take turns. Roll the three number cubes. Find a segment piece to match each number rolled. See whether a triangle can be formed from those segment pieces. The value of the perimeter of any triangle that can be formed is added to that player’s score. The first player to reach 50 points wins.
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Amir wonders what the game has to do with triangles. 1. Play the game above to see how it relates to triangles. Follow the rules. Record your results in the table. Player 1 Numbers
Player 2 Score
Numbers
Player 3 Score
Numbers
Player 4 Score
Numbers
Score
Activity 22 • Angles and Triangles
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Lesson 22-1 Properties of Triangles and Side Lengths
ACTIVITY 22 continued My Notes
2. There is more to the game than just adding numbers. How does the game relate to triangles?
Amir noticed that he could tell whether the lengths would form a triangle even without the segment pieces. 3. Explain how Amir can determine whether a triangle can be formed from three given lengths.
MATH TIP When sides of a figure have the same length, this can be shown by drawing marks, called tick marks, on those sides. For example, the equal sides of the isosceles and equilateral triangles in the table below right have the same number of tick marks.
Matt and Allie’s game illustrates the following property that relates the side lengths of a triangle. Triangle Inequality Property For any triangle, the sum of any two sides must be greater than the length of the third side. Before students play another game, Mr. Mira wants to review the vocabulary terms scalene, isosceles, and equilateral with the class. He draws the following examples of triangles. Isosceles Triangles
Equilateral Triangles
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Scalene Triangles
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Unit 5 • Geometric Concepts
Lesson 22-1 Properties of Triangles and Side Lengths
Activity 22 continued My Notes
4. Based on Mr. Mira’s examples, describe each type of triangle. a. scalene triangle
Math Tip
b. isosceles triangle
A triangle can be identified as scalene, isosceles, or equilateral by the lengths of its sides.
c. equilateral triangle Amir creates a variation of Matt and Allie’s game. Here are the rules for Amir’s game. Triangle Trivia Rules - Name the Triangle Players: Materials: Directions:
Three to four students Three number cubes Take turns rolling three number cubes. • If you can, form a scalene triangle .............add 5 points an isosceles triangle ........add 10 points an equilateral triangle .....add 15 points no triangle ............................add 0 points • If you make a mistake, deduct 10 points from your last correct score. • The first player to reach 25 points wins.
© 2014 College Board. All rights reserved.
5. Make use of structure. When playing Amir’s variation of Triangle Trivia, suppose that the cubes landed on the following numbers. Tell how many points you would add to your score and why. a. 5, 5, 5 b. 1, 6, 4 c. 3, 2, 4 d. 6, 6, 4 e. 1, 4, 1 Share your responses with your group members. Make notes as you listen to other members of your group. Ask and answer questions clearly to aid comprehension and to ensure understanding of all group members’ ideas.
Activity 22 • Angles and Triangles
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Lesson 22-1 Properties of Triangles and Side Lengths
Activity 22 continued My Notes
Check Your Understanding 6. Can a triangle be formed using the side lengths below? If so, is the triangle scalene, isosceles, or equilateral? Explain. a . 4 m, 4 m, and 8 m b. 8 ft, 6 ft, and 4 ft 7. If three segments form a triangle, what must be true about the sum of any two side lengths of the triangle?
Lesson 22-1 Practice For Items 8–14, use the Triangle Inequality Property to determine whether a triangle can be formed with the given side lengths in inches. If a triangle can be formed, classify the triangle by the lengths of its sides. Explain your thinking. 8. a = 5, b = 5, c = 5 9. a = 3, b = 3, c = 7 10. a = 7, b = 4, c = 4 11. a = 8, b = 4, c = 5 12. a = 1, b = 2, c = 8 13. a = 8, b = 12, c = 4 15. Which of the following are possible side lengths of a triangle? A. 12, 20, 15 B . 33, 20, 12 C . 12, 20, 11 16. Reason abstractly. Is it necessary to find the sum of all three possible pairs of side lengths to use the Triangle Inequality Property when deciding if the sides form a triangle? Include an example in your explanation. 17. Construct viable arguments. Two sides of a triangle are 9 and 11 centimeters long. a. What is the shortest possible length for the third side? b. What is the longest possible length for the third side?
280 Unit 5 • Geometric Concepts
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14. a = 12, b = 5, c = 13
