Geometry Section 1-5
- 2. Essential Questions • How do you identify and use special pairs of angles? • How do you identify perpendicular lines?
- 3. Vocabulary 1. Adjacent Angles: 2. Linear Pair: 3. Vertical Angles: 4. Complementary Angles:
- 4. Vocabulary 1. Adjacent Angles: Two angles that share a vertex and side but no interior points 2. Linear Pair: 3. Vertical Angles: 4. Complementary Angles:
- 5. Vocabulary 1. Adjacent Angles: Two angles that share a vertex and side but no interior points 2. Linear Pair: A pair of adjacent angles where the non- shared sides are opposite rays 3. Vertical Angles: 4. Complementary Angles:
- 6. Vocabulary 1. Adjacent Angles: Two angles that share a vertex and side but no interior points 2. Linear Pair: A pair of adjacent angles where the non- shared sides are opposite rays 3. Vertical Angles: Nonadjacent angles that are formed when two lines intersect; only share a vertex 4. Complementary Angles:
- 7. Vocabulary 1. Adjacent Angles: Two angles that share a vertex and side but no interior points 2. Linear Pair: A pair of adjacent angles where the non- shared sides are opposite rays 3. Vertical Angles: Nonadjacent angles that are formed when two lines intersect; only share a vertex 4. Complementary Angles: Two angles with measures such that the sum of the angles is 90 degrees
- 8. Vocabulary 5. Supplementary Angles: 6. Perpendicular:
- 9. Vocabulary 5. Supplementary Angles: Two angles with measures such that the sum of the angles is 180 degrees 6. Perpendicular:
- 10. Vocabulary 5. Supplementary Angles: Two angles with measures such that the sum of the angles is 180 degrees 6. Perpendicular: When two lines, segments, or rays intersect at a right angle
- 11. Adjacent Angles
- 13. Adjacent Angles A B C D m∠ADB + m∠BDC = m∠ADC
- 14. Linear Pair
- 15. Linear Pair 1 2
- 16. Linear Pair 1 2 m∠1+ m∠2 =180°
- 17. Vertical Angles
- 20. Vertical Angles ∠1≅ ∠3 1 2 3 4 ∠2 ≅ ∠4
- 21. Example 1 Name a pair that satisfies each condition. a.A pair of vertical angles b.A pair of adjacent angles c.A linear pair
- 22. Example 1 Name a pair that satisfies each condition. a.A pair of vertical angles ∠AGF and ∠DGC b.A pair of adjacent angles c.A linear pair
- 23. Example 1 Name a pair that satisfies each condition. a.A pair of vertical angles ∠AGF and ∠DGC b.A pair of adjacent angles ∠AGF and ∠FGE c.A linear pair
- 24. Example 1 Name a pair that satisfies each condition. a.A pair of vertical angles ∠AGF and ∠DGC b.A pair of adjacent angles ∠AGF and ∠FGE c.A linear pair ∠AGB and ∠BGD
- 25. Example 1 d.What is the relationship between the following angles? ∠FGB and ∠BGD
- 26. Example 1 d.What is the relationship between the following angles? ∠FGB and ∠BGD These are adjacent angles
- 27. Example 2 Find answers to satisfy each condition. a. Name two complementary angles b. Name two supplementary angles
- 28. Example 2 Find answers to satisfy each condition. a. Name two complementary angles ∠TWU and ∠UWV b. Name two supplementary angles
- 29. Example 2 Find answers to satisfy each condition. a. Name two complementary angles ∠TWU and ∠UWV b. Name two supplementary angles ∠SWT and ∠TWV
- 30. Example 2 Find answers to satisfy each condition. c. If , findm∠RWS = 72° m∠UWV d. If , findm∠RWS = 72° m∠RWV
- 31. Example 2 Find answers to satisfy each condition. m∠UWV = 72° c. If , findm∠RWS = 72° m∠UWV d. If , findm∠RWS = 72° m∠RWV
- 32. Example 2 Find answers to satisfy each condition. m∠UWV = 72° c. If , findm∠RWS = 72° m∠UWV (vertical angles) d. If , findm∠RWS = 72° m∠RWV
- 33. Example 2 Find answers to satisfy each condition. m∠UWV = 72° c. If , findm∠RWS = 72° m∠UWV (vertical angles) d. If , findm∠RWS = 72° m∠RWV 180° − 72°
- 34. Example 2 Find answers to satisfy each condition. m∠UWV = 72° c. If , findm∠RWS = 72° m∠UWV (vertical angles) m∠RWV =108° d. If , findm∠RWS = 72° m∠RWV 180° − 72°
- 35. Example 2 Find answers to satisfy each condition. m∠UWV = 72° c. If , findm∠RWS = 72° m∠UWV (vertical angles) m∠RWV =108° d. If , findm∠RWS = 72° m∠RWV (supplementary angles) 180° − 72°
- 36. Example 2 Find answers to satisfy each condition. f. If , findm∠UWV = 47° m∠UWT e. Name two perpendicular segments
- 37. Example 2 Find answers to satisfy each condition. SW and TW f. If , findm∠UWV = 47° m∠UWT e. Name two perpendicular segments
- 38. Example 2 Find answers to satisfy each condition. SW and TW f. If , findm∠UWV = 47° m∠UWT 90° − 47° e. Name two perpendicular segments
- 39. Example 2 Find answers to satisfy each condition. SW and TW m∠UWT = 43° f. If , findm∠UWV = 47° m∠UWT 90° − 47° e. Name two perpendicular segments
- 40. Example 2 Find answers to satisfy each condition. SW and TW m∠UWT = 43° f. If , findm∠UWV = 47° m∠UWT (complementary angles) 90° − 47° e. Name two perpendicular segments
- 41. Example 3 Find x and y so that AE ⊥ CF .
- 42. Example 3 Find x and y so that AE ⊥ CF . 2x + 14 + 2x = 90
- 43. Example 3 Find x and y so that AE ⊥ CF . 2x + 14 + 2x = 90 4x + 14 = 90
- 44. Example 3 Find x and y so that AE ⊥ CF . 2x + 14 + 2x = 90 4x + 14 = 90 −14 −14
- 45. Example 3 Find x and y so that AE ⊥ CF . 2x + 14 + 2x = 90 4x + 14 = 90 −14 −14 4x = 76
- 46. Example 3 Find x and y so that AE ⊥ CF . 2x + 14 + 2x = 90 4x + 14 = 90 −14 −14 4x = 76 4 4
- 47. Example 3 Find x and y so that AE ⊥ CF . 2x + 14 + 2x = 90 4x + 14 = 90 −14 −14 4x = 76 4 4 x = 19
- 48. Example 3 Find x and y so that AE ⊥ CF . 2x + 14 + 2x = 90 4x + 14 = 90 −14 −14 4x = 76 4 4 x = 19 8y + 10 = 90
- 49. Example 3 Find x and y so that AE ⊥ CF . 2x + 14 + 2x = 90 4x + 14 = 90 −14 −14 4x = 76 4 4 x = 19 8y + 10 = 90 −10 −10
- 50. Example 3 Find x and y so that AE ⊥ CF . 2x + 14 + 2x = 90 4x + 14 = 90 −14 −14 4x = 76 4 4 x = 19 8y + 10 = 90 −10 −10 8y = 80
- 51. Example 3 Find x and y so that AE ⊥ CF . 2x + 14 + 2x = 90 4x + 14 = 90 −14 −14 4x = 76 4 4 x = 19 8y + 10 = 90 −10 −10 8y = 80 8 8
- 52. Example 3 Find x and y so that AE ⊥ CF . 2x + 14 + 2x = 90 4x + 14 = 90 −14 −14 4x = 76 4 4 x = 19 8y + 10 = 90 −10 −10 8y = 80 8 8 y = 10
- 53. Example 4 Find the measures of two supplementary angles so that the difference between the measures of the two angles is 44. x° (180 − x)°
- 54. Example 4 Find the measures of two supplementary angles so that the difference between the measures of the two angles is 44. x° (180 − x)° (180 − x) − x = 44
- 55. Example 4 Find the measures of two supplementary angles so that the difference between the measures of the two angles is 44. x° (180 − x)° (180 − x) − x = 44 180 − 2x = 44
- 56. Example 4 Find the measures of two supplementary angles so that the difference between the measures of the two angles is 44. x° (180 − x)° (180 − x) − x = 44 180 − 2x = 44 −180 −180
- 57. Example 4 Find the measures of two supplementary angles so that the difference between the measures of the two angles is 44. x° (180 − x)° (180 − x) − x = 44 180 − 2x = 44 −180 −180 −2x = −136
- 58. Example 4 Find the measures of two supplementary angles so that the difference between the measures of the two angles is 44. x° (180 − x)° (180 − x) − x = 44 180 − 2x = 44 −180 −180 −2x = −136 −2 −2
- 59. Example 4 Find the measures of two supplementary angles so that the difference between the measures of the two angles is 44. x° (180 − x)° (180 − x) − x = 44 180 − 2x = 44 −180 −180 −2x = −136 −2 −2 x = 68°
- 60. Example 4 Find the measures of two supplementary angles so that the difference between the measures of the two angles is 44. x° (180 − x)° (180 − x) − x = 44 180 − 2x = 44 −180 −180 −2x = −136 −2 −2 x = 68° 180 − 68
- 61. Example 4 Find the measures of two supplementary angles so that the difference between the measures of the two angles is 44. x° (180 − x)° (180 − x) − x = 44 180 − 2x = 44 −180 −180 −2x = −136 −2 −2 x = 68° 180 − 68 =112°
- 62. Example 4 Find the measures of two supplementary angles so that the difference between the measures of the two angles is 44. x° (180 − x)° (180 − x) − x = 44 180 − 2x = 44 −180 −180 −2x = −136 −2 −2 x = 68° 180 − 68 =112° The two angles are 68° and 112°