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Chapter Review CHAPTER 7 7-1 Angle Relationships Use the diagram to name each geometric figure. Q R 70° P 90° T 20° S 1. two obtuse angles 2. two acute angles In the figure, ⬔1 and ⬔3 are vertical angles, and ⬔2 and ⬔4 are vertical angles. 3. If m⬔2 ⫽ 100°, find m⬔1. 1 2 4 3 4. If m⬔2 ⫽ 100°, find m⬔4. 7-2 Parallel and Perpendicular Lines c In the figure, line a 冷冷 line b. 1 2 3 a 4 5 6 7 5. Name all angles congruent to ⬔6. b 8 6. Name all angles congruent to ⬔8. 7. Which line is the transversal? 8. Name three pairs of supplementary angles. 7-3 Triangles Find the value of each variable. 9. 10. 31° 11. w° y° 2w° x° Copyright © by Holt McDougal. All rights reserved. 30° (3y + 10)° 31° 161 Holt McDougal Mathematics CHAPTER 7 REVIEW CONTINUED 7-4 Polygons Find the sum of the angle measures of each polygon. Then, if the polygon is regular, find the measure of each angle. 12. 14-gon 13. 13-gon 14. octagon Find the value of each variable. 15. 120° x° 50° 130° 16. 105° 17. 145° 90° 32° 162° 122° 95° y° w° 77° 105° 7-5 Coordinate Geometry Find the coordinates of the midpoint of each segment. 18. 19. y A 4 3 2 1 O ⴚ4ⴚ3 –2 ⴚ1 ⴚ1 ⴚ2 ⴚ3 ⴚ4 y Y x 4 3 2 1 O ⴚ4ⴚ3 –2 ⴚ1 ⴚ1 ⴚ2 ⴚ3 ⴚ4 X 1 2 3 4 B x 1 2 3 4 7-6 Congruence Z Write a congruence statement for each pair of polygons. 20. 21. F H 36° 121° D E 121° 62° Q 58° I 23° 120° P G 120° W R 60° 120° X S Y Copyright © by Holt McDougal. All rights reserved. 162 Holt McDougal Mathematics CHAPTER 7 REVIEW CONTINUED 7-7 Transformations 22. Graph a reflection across the x-axis. y y B 4 3 2 1 A O ⴚ4ⴚ3 –2 ⴚ1 ⴚ1 ⴚ2 ⴚ3 ⴚ4 4 3 2 1 C x x O ⴚ4ⴚ3 –2 ⴚ1 ⴚ1 ⴚ2 ⴚ3 ⴚ4 1 2 3 4 4 3 2 1 O ⴚ4ⴚ3 –2 ⴚ1 ⴚ1 B A y B A 23. Graph a rotation 90° clockwise about the origin. 2 3 4 D C y 4 3 2 1 C x x O ⴚ4ⴚ3 –2 ⴚ1 ⴚ1 ⴚ2 ⴚ3 ⴚ4 1 2 3 4 ⴚ2 ⴚ3 ⴚ4 B A 2 3 4 D C 7-8 Symmetry Complete each figure. The dashed line is the line of symmetry. 24. 25. 26. Complete each figure. The point is the center of rotation. 27. 4-fold Copyright © by Holt McDougal. All rights reserved. 28. 2-fold 163 Holt McDougal Mathematics CHAPTER Big Ideas 7 Answer these questions to summarize the important concepts from Chapter 7 in your own words. 1. Explain the difference between complementary angles and supplementary angles. 2. If ⬔1 is 50°, explain how to find m⬔5. 2 1 3 4 5 6 7 8 3. If the measures of two angles in a triangle are 43° and 74°, explain how to find the measure of the third angle. 4. Explain how to rotate a figure with vertices A(–1, 5), B(4, 5), C(4, –2), and D(–1, –2) 90° counterclockwise about the origin. Give the coordinates of the image. For more review of Chapter 7: • Complete the Chapter 7 Study Guide and Review on pages 380–382 of your textbook. • Complete the Ready to Go On quizzes on pages 358 and 376 of your textbook. Copyright © by Holt McDougal. All rights reserved. 164 Holt McDougal Mathematics Chapter Review CHAPTER 7 7-1 Angle Relationships Use the diagram to name each geometric figure. Q R 70° P 90° T 20° S 1. two obtuse angles 2. two acute angles ⬔QTS, ⬔PTR ⬔PTQ, ⬔RTS In the figure, ⬔1 and ⬔3 are vertical angles, and ⬔2 and ⬔4 are vertical angles. 3. If m⬔2 100°, find m⬔1. m⬔1 80° 4. If m⬔2 100°, find m⬔4. m⬔4 100° 1 2 4 3 7-2 Parallel and Perpendicular Lines c In the figure, line a line b. 1 5. Name all angles congruent to ⬔6. ⬔2, ⬔3, ⬔7 6. Name all angles congruent to ⬔8. ⬔1, ⬔4, ⬔5 7. Which line is the transversal? 2 3 a 4 5 6 7 b 8 line c 8. Name three pairs of supplementary angles. 7-3 Triangles Possible answers: ⬔1 and ⬔2, ⬔1 and ⬔3, ⬔3 and ⬔4 Find the value of each variable. 9. 10. 31° 11. w° y° 2w° x° x 118° Copyright © by Holt McDougal. All rights reserved. (3y + 10)° 30° 31° w 30° y 35° 161 Holt McDougal Mathematics CHAPTER 7 REVIEW CONTINUED 7-4 Polygons Find the sum of the angle measures of each polygon. Then, if the polygon is regular, find the measure of each angle. 12. 14-gon 13. 13-gon 2160°; 154.3° 14. octagon 1980°; 152.3° 1080°; 135° Find the value of each variable. 15. 120° x° 50° 130° 16. 105° 17. 145° 90° 32° 162° 122° 95° y° x 85° w° 77° 105° y 155° w 147° 7-5 Coordinate Geometry Find the coordinates of the midpoint of each segment. 18. 19. y A 4 3 2 1 O ⴚ4ⴚ3 –2 ⴚ1 ⴚ1 ⴚ2 ⴚ3 ⴚ4 y Y x O ⴚ4ⴚ3 –2 ⴚ1 ⴚ1 ⴚ2 ⴚ3 ⴚ4 X 1 2 3 4 12 , 12 B 4 3 2 1 x 1 2 3 4 (2, 1) 7-6 Congruence Z Write a congruence statement for each pair of polygons. 20. 21. F H 121° 36° 121° D E 62° Q 58° I 23° 120° P G 120° W R 60° 120° X S Y quadrilateral PQRS quadrilateral XYZW triangle DEF triangle HGI Copyright © by Holt McDougal. All rights reserved. 162 Holt McDougal Mathematics CHAPTER 7 REVIEW CONTINUED 7-7 Transformations 22. Graph a reflection across the x-axis. y y B 4 3 2 1 A 23. Graph a rotation 90° clockwise about the origin. O ⴚ4ⴚ3 –2 ⴚ1 ⴚ1 ⴚ2 ⴚ3 ⴚ4 4 3 2 1 C x y B 4 3 2 1 A O A' ⴚ4ⴚ3 –2 ⴚ1 ⴚ1 ⴚ2 ⴚ3 ⴚ4 x O ⴚ4ⴚ3 –2 ⴚ1 ⴚ1 ⴚ2 ⴚ3 ⴚ4 1 2 3 4 B A 2 3 4 D C y 4 3 2 1 C x A B x O ⴚ4ⴚ3 –2 ⴚ1 2 3 4 ⴚ1 A' ⴚ2 ⴚ3 ⴚ4 D B' C C' 1 2 3 4 C' B' 7-8 Symmetry Complete each figure. The dashed line is the line of symmetry. 24. 25. 26. Complete each figure. The point is the center of rotation. 27. 4-fold Copyright © by Holt McDougal. All rights reserved. 28. 2-fold 163 Holt McDougal Mathematics CHAPTER Big Ideas 7 Answer these questions to summarize the important concepts from Chapter 7 in your own words. 1. Explain the difference between complementary angles and supplementary angles. Complementary angles are angles whose sum measures add to 90°. Supplementary angles are angles whose sum measures add to 180°. 2. If ⬔1 is 50°, explain how to find m⬔5. ⬔1 ⫽ 50° so ⬔6 ⫽ 50° because corresponding angles are congruent. ⬔6 and ⬔5 are supplementary angles, therefore 180° ⫺ m⬔6 ⫽ m⬔5; 180° ⫺ 50° ⫽ 130°. m⬔5 ⫽ 130°. 2 1 3 4 5 6 7 8 3. If the measures of two angles in a triangle are 43° and 74°, explain how to find the measure of the third angle. The Triangle Sum Theorem states that the angle measures of a triangle add to 180°. Two of the three angle measures are known, so subtract the known angle measures from 180°: 180° ⫺ 43° ⫺ 74° ⫽ 63°. The measure of the third angle in the triangle is 63°. 4. Explain how to rotate a figure with vertices A(–1, 5), B(4, 5), C(4, –2), and D(–1, –2) 90° counterclockwise about the origin. Give the coordinates of the image. Multiply each y-coordinate by –1, and then switch the x- and y-coordinates: A’ (⫺1, ⫺1 • 5) → A’ (⫺1, ⫺5) → A’ (⫺5, ⫺1); B’ (4, ⫺1 • 5) → B’ (4, ⫺5) → B’ (⫺5, 4); C’ (4, ⫺1 • ⫺2) → C’ (4, 2) → C’ (2, 4); D’ (⫺1, ⫺1 • ⫺2) → D’ (⫺1, 2) → D’ (2, ⫺1). For more review of Chapter 7: • Complete the Chapter 7 Study Guide and Review on pages 380–382 of your textbook. • Complete the Ready to Go On quizzes on pages 358 and 376 of your textbook. Copyright © by Holt McDougal. All rights reserved. 164 Holt McDougal Mathematics