SUGGESTED LEARNING STRATEGIES:

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1 Lesson 22-2 ACTIVITY 22 Learning Targets: Classify angles by their measures. Classify triangles by their angles. Recognize the relationship between the lengths of sides and measures of angles in a triangle. Recognize the sum of angles in a triangle. SUGGESTED LEARNING STRATEGIES: Interactive Word Wall, Summarizing, Visualization, Graphic Organizer MATH TIP If the rays are too short to measure with a protractor, extend the length of the sides of the angle. Another way to classify triangles is by their angles. A right angle has a measure of. An acute angle has a measure of less than. An obtuse angle is greater than and less than Use the angles shown. C A B D E F a. Estimate the measure of each angle. A B C D E F b. Use appropriate tools strategically. Use a protractor to find the measure of each angle to the nearest degree. Then classify each angle as acute, obtuse, or right by its measure. A = B = C = D = E = F = Activity 22 Angles and Triangles 281

2 Activity 22 Lesson 22-2 Now Mr. Mira draws the following examples of triangles. Math Tip Acute Triangles Obtuse Triangles Right Triangles A box at the vertex of an angle indicates an angle with measure. A E I B D G C F H 2. Based on Mr. Mira s examples, describe each type of triangle. a. acute triangle b. obtuse triangle c. right triangle 3. A triangle can be labeled using both its angle measure and the lengths of its sides. a. Label the triangles that Mr. Mira drew by side length. b. Choose one of the triangles and give the two labels that describe it. c. Explain how the two labels together provide a better description of the triangle than either one alone. Share your ideas with our group and be sure to explain your thoughts using precise language and specific details to help group members understand your ideas and reasoning. 282 Unit 5 Geometric Concepts

3 Lesson 22-2 Activity 22 Mr. Mira has his class investigate the sum of the measures of a triangle. Students measured the angles of some scalene, isosceles, and equilateral triangles. They recorded their results as shown. Scalene Triangles Isosceles Triangles Equilateral Triangles a. Find the sum of the angle measures for each triangle. The Triangle Sum Theorem states that the sum of the three angle measures in any triangle is always equal to a certain number. b. What is the sum of the angle measures in any triangle? MATH TERMS A theorem is a statement or conjecture that has been proven to be true. Activity 22 Angles and Triangles 283

4 Activity 22 Lesson 22-2 The Triangle Sum Theorem allows you to find the measure of the third angle in a triangle when you are given the other two angle measures. 5. Students played a game in which they chose two angle measures of a triangle and then determined the third angle measure. What must be true about the two angle measures the students choose? 6. Some of the angle measures students created for triangles are shown. For each pair of angle measures, find the measure of the third angle in the triangle. a. 43, 94 b. 38, 52 c. 57, 39 d. 1, 12 e., 284 Unit 5 Geometric Concepts

5 Lesson 22-2 Activity 22 The angle measures of a triangle can be used to determine if the triangle is scalene, isosceles, or equilateral. Look back at the triangles Mr. Mira drew. Scalene Triangles Isosceles Triangles Equilateral Triangles Compare the angle measures of the triangles. Look for patterns in Mr. Mira s examples to help you determine if the triangles described below are scalene, isosceles, or equilateral. a. a triangle with three different angle measures b. a triangle with exactly two congruent angle measures c. an equiangular triangle Math TERMS A triangle with three equal angles is called equiangular. 8. Look back at Item 6. Classify each triangle by its side length and by its angle measure. Another relationship exists between the angles and the sides of a triangle. In a triangle, the side opposite the angle with the greatest measure is the longest side. 9. Compare the angle measure to the side opposite the angle in a scalene triangle. What is true about the side opposite the angle with the least measure? Activity 22 Angles and Triangles 285

6 ACTIVITY 22 Lesson 22-2 Check Your Understanding For Items 10 12, sketch a triangle described by each pair of words below or state that it is not possible. Use tick marks and right angle symbols where appropriate. If it is not possible to sketch a triangle, explain why not. 10. scalene, obtuse 11. isosceles, acute 12. equilateral, right 13. Two angles in a triangle measure 35 and 50. Explain how to find the measure of the third angle. LESSON 22-2 PRACTICE For Items 14 19, sketch a triangle described by each pair of words below or state that it is not possible. If it is not possible to sketch a triangle, explain why not. 14. scalene, right 15. isosceles, obtuse 16. equilateral, acute 17. isosceles, right 18. scalene, acute 19. equilateral, obtuse 20. Use appropriate tools strategically. Use a ruler and a protractor to sketch a triangle that is scalene and has an angle that measures. Is the triangle acute, right, or obtuse? Explain. 21. Two angles in a triangle measure 65 each. What is the measure of the third angle? 22. Reason quantitatively and abstractly. Find the missing angle measure or measures in each triangle below. Then classify the triangle by both its angle measures and its side lengths. a. The three angles in a triangle have the same measure. b. Two angles in a triangle measure each. c. Two angles in a triangle measure 25 and Construct viable arguments. Determine whether each statement below is always true, sometimes true, or never true. Explain your reasoning. a. The acute angles of an isosceles triangle add up to. b. An isosceles triangle has two equal angles. c. An equilateral triangle has a right angle. d. The largest angle of a scalene triangle can be opposite the shortest side. 286 Unit 5 Geometric Concepts