Demo slides in math editedppt
- 2. Dear Lord, We thank you a hundredfold for the love and care that you have given us. May we return to you, your good works by multiplying it with love and respect, adding more faith, subtracting the unworldly behavior and evil works and dividing your given talents to others so we can sum it all and be united as one, in your family. In this we pray, Amen.
- 3. WARM-UP ACTIVITY Find the measure of the missing angle without using a protractor.
- 4. 48°?
- 5. 48°48°
- 6. 155° ?
- 7. 155° 25°
- 8. 30° ?
- 9. 30° 60°
- 10. 50° ?
- 11. 40° 50°
- 12. 28° ?
- 13. 28° 152°
- 15. P ____ ____ ____
- 16. P A I R
- 17. I ___ ___ ___ R ___ ___ R
- 18. I N T E R I O R
- 19. P ___ ___ ___ ___ ___ ___ ___
- 20. P A R A L L E L
- 21. V ___ ___ ___ ___ ___ ___ L
- 22. V E R T I C A L
- 23. T ___ ___ ___ ___ V ___ ___ ___ ___ L
- 24. T R A N S V E R S A L
- 25. A A ___ ___ ___ ___
- 26. A N G L E
- 27. E X ___ ___ ___ ___ ___ R
- 28. E X T E R I O R
- 29. PROPERTIES OF PARALLEL LINES CUT BY A TRANSVERSAL
- 30. Parallel lines are coplanar lines that never intersect.
- 31. Transversal is a line that intersects two or more lines at different points.
- 32. 3 1 2 4 6 57 8 “ Lines and Angles”
- 33. Postulate If two parallel lines are cut by a transversal then the corresponding angles are congruent.
- 34. Given : a II b transversal t cuts lines a and b Prove : Statement 1. a II b 2. <1 = <2 3. 4. Reason 1. Given 2. 3. 4. Transitive Property a b t 12 34
- 35. Theorem If two parallel lines are cut by transversal , then alternate interior angles are congruent.
- 37. Theorem If two parallel lines are cut by transversal , then alternate exterior angles are congruent.
- 39. Given : a II b transversal t cuts lines a and b Prove : are supplementary. t a b 1 2 3 4 Statement Reason 1. a II b 2. 3. 4. 5. 6. 7. 1. Given 2. Linear Pair Postulate 3. 4. 5. 6. 7. Definition of Supplementary Angles
- 40. Theorem If two parallel lines are cut by a transversal, then the interior angles on the same side of the transversal are supplementary.
- 42. Theorem If two parallel lines are cut by a transversal, then the exterior angles on the same side of the transversal are supplementary.
- 44. Determine whether the following pairs of angles are congruent or supplementary.
- 49. Illustrative Examples Given :s II t, m 1 = 5x + 9 and m 2 = 3x +11. Find x and the m 1 and m 2. 1 2
- 50. Given : a II b, m 1 = 4x-7 and m 2 = 2x +19. Find x and the m 1 and m 2. a b t 1 2
- 51. GROUP ACTIVITY
- 52. 1.In the given figure, find the measure of the numbered angles if m 1 = 120° 1 4 3 2 5 6 7 8
- 53. In the given figure find the measure of the numbered angles if m 1 = 120° 120° 60° 60° 120° 120° 120° 60° 60°
- 54. 2.Solve for x given that a II b, then find the measure of angle 1 and 8 if m 1= 2x+25 and m 8 = x + 75. 5 6 7 8 1 2 3 4
- 55. Answer x = 50 measure of angle 1=125° measure of angle 8 = 125°
- 56. 2x + 4 l1 l2 110° If || , find x.1 2l l
- 57. Answer x = 53
- 58. Solve for x given that a II b, then find the measure of angle 6 and 1 if m 6= 4x+ 10 and m 1 = 6x +10. 5 6 7 8 1 2 3 4
- 59. Solve for x given that a II b, then find the measure of angle 6 and 1 if m 6= 4x+ 10 and m 1 = 6x +10. 5 74° 7 8 106° 2 3 4 x = 16
- 60. QUIZ
- 61. I. Directions: Identify the following pairs of whether congruent or supplementary. 1. 8 and 6 2. 2 and 7 3. 4 and 8 7 4. 3 and 5 8 5. 1 and 8 5 6 3 1 4 2
- 62. 1. Find the measure of the numbered angles if a II b and the measure of one angle is given. 2 3 47° II.
- 63. 2. Find the value of x for which a II b. 4x° 108°
- 64. 3. Find the value of x for which a II b. 50° (3x + 10)°
- 65. 4.Solve for x given that a II b, then find the measure of angle 7 and 4 if m 7= 2x -15 and m 4 = x + 17. 5 6 7 8 1 4 3 2
- 66. ANSWER II.1. 2 = 133°, 3= 133° 2. X = 27 3. X= 40 4. X = 32, 7 = 49°, 4 = 49°
- 67. ASSIGNMENT Study the problem situation in Activity 6 on page 453 ( Learner's Material ), then answer the given questions using the sketch.
- 68. LIFE is a math equation. In order to gain the most, you have to know how to convert negatives into positives. - Anonymous-
- 69. Geometry Opportunity is missed by most people because it is dressed in overalls and looks like work. Thomas Edis Today: •Homework Check •3.2 Check Up •Practice
- 70. Yesterday Assignment: • 3.1-3.2 p. 197 #1-14 Opportunity is missed by most people because it is dressed in overalls and looks like work. Thomas Edison
- 71. Identify the vocabulary term for each pair of angles represented in the picture. 1. ∠3 and ∠6 2. ∠1 and ∠8 3. ∠2 and ∠6 4. ∠1 and ∠6 5. ∠3 and ∠5 3.2 Check Up
- 72. You named angle pairs formed by parallel lines and transversals. • Use theorems to determine the relationships between specific pairs of angles. • Use algebra to find angle measurements.
- 73. Content Standards G.CO.1 Know precise definitions of angle, circle, perpendicular line, parallel line, and line segment, based on the undefined notions of point, line, distance along a line, and distance around a circular arc. G.CO.9 Prove theorems about lines and angles. Mathematical Practices 1 Make sense of problems and persevere in solving them. 3 Construct viable arguments and critique the reasoning of others.
- 74. 3.2 Angles and Parallel Lines Objectives: 1. Properties of parallel lines and transversals 2. Using properties of parallel lines in proofs Vocabulary: parallel, transversal, corresponding, alternate interior, alternate exterior, consecutive interior
- 75. If 2 parallel lines are cut by a transversal, then: corresponding angles are congruent. alternate interior angles are congruent. alternate exterio corresponding angles alternate interior angles alternate ex 1 2 4 3 5 6 8 7 3.2 Angles and Parallel Lines
- 76. 2x + 4 l1 l2 110° If || , find x.1 2l l
- 77. If || , find x and y.1 2l l y + 20 l1 l2 °75 x x = 105 y = 85
- 79. Given: || || Prove: 1 2 1 3 l l l l 2 4 ∠ ≅ ∠ 1 3 2 Statements Reasons 1. Given ALWAYS 4. Transitive Property of Congruency.
- 80. Geometry Assignment: • 3.2 p. 183 #5, 8, 25, 49 Opportunity is missed by most people because it is dressed in overalls and looks like work. Thomas Edison