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3-1 NAME ______________________________________DATE __________PERIOD______ Practice Student Edition Pages 90–94 Angles Name each angle in four ways. Then identify its vertex and its sides. 1. 2. ⬔LMN, ⬔NML, ⬔M, and ⬔7 3. ⬔OPQ, ⬔QPO, ⬔P, and ⬔8 ⬔RST, ⬔TSR, ⬔S and ⬔9 Name all angles having Q as their vertex. 4. 5. ⬔1, ⬔2, and ⬔UQW 6. ⬔3, ⬔4, ⬔XQZ ⬔5, ⬔6, ⬔7, ⬔AQC, ⬔BQD, and ⬔AQD Tell whether each point is in the interior, exterior or on the angle. 7. 8. interior 10. interior 9. exterior 11. on 12. on exterior Tell whether each statement is true or false. 13. The vertex is in the exterior of the angle. false 14. ⬔ABC, ⬔CBA, and ⬔B are all the same angle. true 15. Three rays are necessary to determine an angle. false © Glencoe/McGraw-Hill T12 Geometry: Concepts and Applications NAME ______________________________________DATE __________PERIOD______ 3-2 Practice Student Edition Pages 96–101 Angle Measure Use a protractor to find the measure of each angle. Then classify each angle as acute, obtuse, or right. 1. ⬔JHI 40; acute 2. ⬔KHI 90; right 3. ⬔MHI 130; obtuse 4. ⬔LHI 110; obtuse 5. ⬔LHM 20; acute 6. ⬔LHK 20; acute 7. ⬔MHJ 90; right 8. ⬔MHK 40; acute 9. ⬔KHJ 50; acute 10. ⬔LHJ 70; acute Use a protractor to draw an angle having each measurement. Then classify each angle as acute, obtuse, or right. See student’s work. 11. 32° acute 12, 178° obtuse 13. 105° obtuse 14. 92° obtuse 15. 80° acute 16. 15° acute 17. 29° acute 18. 150° obtuse 19. 163° obtuse 20. 120° obtuse © Glencoe/McGraw-Hill T13 Geometry: Concepts and Applications 3-3 NAME ______________________________________DATE __________PERIOD______ Practice Student Edition Pages 104–109 The Angle Addition Postulate Refer to the figure at the right. 1. If m⬔BFC 35 and m⬔AFC 78 find m⬔1. 43 2. If m⬔BFC 20 and m⬔CFD 37 find m⬔BFD. 57 bisects ⬔BFD, find ⬔CFD. 3. If m⬔BFD 60 and FC 30 4. If m⬔AFB 70 and m⬔BFC 15, find m⬔AFC. 85 5. If m⬔DFE 18 and m⬔CFE 45, find ⬔CFD. 27 Refer to the figure at the right. 6. If m⬔3 45 and m⬔JLI 20, find m⬔ILK. 65 7. If m⬔GLJ 90, m⬔GLH 30, and m⬔HLI 30, find m⬔ILJ. 30 8. If m⬔HLJ 70 and m⬔GLJ 90, find m⬔GLH. 20 9. If m⬔3 40 and m⬔JLH 60, find m⬔KLH. 100 10. If m⬔GLI 62 and m⬔GLH 40, find m⬔HLI. 22 11. If a right angle is bisected, what type of angles are formed? acute 12. What type of angles are formed if a 40° angle is bisected? acute 13. If m⬔1 30, m⬔2 3x, m⬔ABC 145, and m⬔3 5x 5, find x. 15 © Glencoe/McGraw-Hill T14 Geometry: Concepts and Applications 3-4 NAME ______________________________________DATE __________PERIOD______ Practice Student Edition Pages 110–114 Adjacent Angles and Linear Pairs of Angles Use the terms adjacent angles, linear pair, or neither to describe angles 1 and 2 in as many ways as possible. 1. 2. 3. adjacent angles; linear pair neither neither 4. 5. neither 6. adjacent angles; linear pair adjacent and GF are opposite In the figure at the right GB and GD are opposite rays. rays and GA 7. Which angle forms a linear pair with ⬔AGC? ⬔CGD 8. Do ⬔FGE and ⬔EGC form a linear pair? Justify your answer. No; they do not contain sides that are opposite rays. 9. Name two angles that are adjacent angles. Sample answer: ⬔DGE and ⬔EGF 10. Name three angles that are adjacent to ⬔EGD. Sample answer: ⬔DGC, ⬔DGB, ⬔EGA 11. Which angle forms a linear pair with ⬔BGC? ⬔CGF 12. Name two adjacent angles that form a linear pair. Sample answer: ⬔AGB and ⬔AGF © Glencoe/McGraw-Hill T15 Geometry: Concepts and Applications 3-5 NAME ______________________________________DATE __________PERIOD______ Practice Student Edition Pages 116–121 Complementary and Supplementary Angles Refer to the figures at the right. 1. Name an angle supplementary to ⬔CBD. ⬔DBE 2. Name a pair of adjacent supplementary angles. Sample answer: ⬔CBA, ⬔ABE Exercises 1–3 3. Name an angle complementary to ⬔CBF. ⬔FBG 4. Name two angles that are complementary. Sample answer: ⬔XQZ, ⬔ZQS 5. Find the measure of an angle that is supplementary to ⬔XQZ. 140 6. Find the measure of the complement of ⬔VQY. 50 Exercises 4–7 7. Name two angles that are supplementary. Sample answer ⬔ZQX, ⬔XQV 8. Name an angle complementary to ⬔MON. ⬔MOL 9. Name an angle supplementary to ⬔POQ. ⬔POL 10. Find the measure of ⬔NOP. 70 Exercises 8–10 © Glencoe/McGraw-Hill T16 Geometry: Concepts and Applications 3-6 NAME ______________________________________DATE __________PERIOD______ Practice Student Edition Pages 122–127 Congruent Angles Find the value of x in each figure. 1. 2. 55 4. 3. 110 47 5. 6. 52 43 25 7. What is the measure of an angle that is supplementary to ⬔HIJ if ⬔HIJ ⬵ ⬔KLM? 126 8. If ⬔2 is complementary to ⬔3, ⬔1 is complementary to ⬔2, and m⬔1 35, what are m⬔2 and m⬔3? 55, 35 9. What is the value of x if ⬔PQR and ⬔SQT are vertical angles and m⬔PQR 47 and m⬔SQT 3x 2? 15 10. Find the measure of an angle that is supplementary to ⬔B if the measure of ⬔B is 58. 122 © Glencoe/McGraw-Hill T17 Geometry: Concepts and Applications 3-7 NAME ______________________________________DATE __________PERIOD______ Practice Student Edition Pages 128–133 Perpendicular Lines AG ⊥ CE , AC ⊥ BF and point B is the midpoint of AC . Determine whether the following is true or false. 1. ⬔1 ⬵ ⬔CBD true 2. ⬔1 is a right angle. true 3. ⬔2 and ⬔3 are complementary angles. false 4. m⬔GDF m⬔FDE 90 5. ⬔1 ⬵ ⬔5 true true is the only line perpendicular 6. AC at B. true to BF 7. ⬔3 is an acute angle. false 8. ⬔1 ⬵ ⬔2 false 9. ⬔2 ⬵ ⬔6 true . true is perpendicular to DE 10. AG 11. Name four right angles. Sample answer: ⬔1, ⬔5, ⬔CBD, ⬔EDG 12. Name a pair of supplementary angles. Sample answer: ⬔2 and ⬔3 13. If m⬔3 120, find m⬔2. 60 14. Which angle is complementary to ⬔FDE? ⬔GDF 15. If m⬔6 45, find m⬔2. © Glencoe/McGraw-Hill 45 T18 Geometry: Concepts and Applications