Angles created by transversal and paralle
- 1. Ms. Johnson 8th Grade math
- 2. Parallel lines: Lines that are the same distance apart over their entire length
- 3. Parallel lines: Lines that are the same distance apart over their entire length Transversal: a line that crosses two other lines
- 4. Parallel lines: Lines that are the same distance apart over their entire length Transversal: a line that crosses two other lines
- 5. When you have a transversal cutting across parallel lines certain relationships are formed
- 6. Lines l and m are parallel. l||m Note the 4 angles that measure 120°. 120° 120° l 120° 120° m Line n is a transversal. n
- 7. Lines l and m are parallel. l||m Note the 4 angles that measure 60°. 60° 60° l 60° 60° m Line n is a transversal. n
- 8. Lines l and m are parallel. l||m There are many There are 4 pairs of pairs of angles that angles that are are supplementary. vertical. 60° 120° 120° 60° l 60° 120° 120° 60° m Line n is a transversal. n
- 10. 9) Lines l and m are parallel. l||m Find the missing angles. 42° a° c° b° l d° e° g° f° m
- 11. 9) Lines l and m are parallel. l||m Find the missing angles. 42° 138° 138° 42° l 42° 138° 138° 42° m
- 12. 10) Lines l and m are parallel. l||m Find the missing angles. 81° a° c° b° l d° e° g° f° m
- 13. 10) Lines l and m are parallel. l||m Find the missing angles. 81° 99° 99° 81° l 81° 99° 99° 81° m
- 14. Sowe know that given a transversal cutting 2 parallel lines, certain relationships are formed. Some of the angles are supplementary because they are on a straight line. And some angles are vertical and thus equal.
- 15. But in this picture, how did we know that the angles highlighted in red are the same???? 120° 120° l 120° 120° m Line n is a transversal. n
- 16. We knew because there are angle relationships of equality besides the vertical angle theorem.. Congruent Angle Relationships (=): Vertical Alternate Interior (AI) Alternate Exterior (AE) Corresponding
- 17. We knew because there are angle relationships of equality besides the vertical angle theorem.. Congruent Angle Relationships (=): Vertical Alternate Interior (AI) Alternate Exterior (AE) Corresponding Ifthe angles in the scenario are not equal to each other, then they are supplementary!!
- 18. The easiest way to see these relationships: Imagine a sandwich. The parallel lines are the bread. The transversal is the toothpick.
- 19. Vertical angles: are on the same slice of “bread” on different sides of the “toothpick.”
- 20. Alternate Interior angles: are inside the “bread”, on opposite sides of the “toothpick.”
- 21. Alternate Interior angles: are inside the “bread”, on opposite sides of the “toothpick.” Alternate Exterior angles: are outside the “bread,” on opposite sides of the “toothpick.”
- 22. Corresponding angles: are on different slices of “bread,” on the same side of the toothpick. Angles are in the same position (both are top left, top right, bottom left, or bottom right). It’s almost like you put one slice of bread on top of the other.
- 23. We actually already know how to find the missing angle using algebra. First, identify the relationship.
- 24. We actually already know how to find the missing angle using algebra. First, identify the relationship. Second, write the equation. If it’s any of these: Vertical (V) Alternate exterior (AE) Alternate interior (AI) Corresponding (C) Then use the same equation you do for all equal relationships. Angle = Angle (the sneaker) And solve for x. Substitute if necessary.
- 25. We actually already know how to find the missing angle using algebra. First, identify the relationship. Second, write the equation. If it’s NOT any of these: Vertical (V) Alternate exterior (AE) Alternate interior (AI) Corresponding (C) Then the relationship has to be supplementary, so the equation is Angle + Angle = 180 (“the boot”) And solve for x. Substitute if necessary.
- 26. Use Algebra to Find Missing Angles Ex. 1 Find x and the unknown angle. 120° (2x)°
- 27. Find x and the unknown angle. 120° (2x)° First, we identify the relationship:
- 28. Find x and the unknown angle. 120° (2x)° First, we identify the relationship: Alternate Interior
- 29. Find x and the unknown angle. 120° (2x)° First, we identify the relationship: Alternate Interior which means the angles are congruent (=)
- 30. Find x and the unknown angle. 120° (2x)° 2x = 120
- 31. Find x and the unknown angle. 120° (2x)° 2x = 120 2 2
- 32. Find x and the unknown angle. 120° (2x)° 2x = 120 • 2 x = 60
- 33. Find x and the unknown angle. 120° (2x)° Now to find the unknown angle, we can just substitute back in. We need to find what angle 2x equals….. 2(60) = 120 So the unknown angle is 120°
- 34. Example 2 Find x and the unknown angle. 2x + 20 70°
- 35. Example 2 Find x and the unknown angle. 2x + 20 70° First we identify the relationship.
- 36. Example 2 Find x and the unknown angle. 2x + 20 70° First we identify the relationship. Corresponding
- 37. Example 2 Find x and the unknown angle. 2x + 20 70° First we identify the relationship. Corresponding So angle = angle
- 38. Example 2 Find x and the unknown angle. 2x + 20 70° Corresponding 2x + 20 = 70
- 39. Example 2 Find x and the unknown angle. 2x + 20 70° Corresponding 2x + 20 = 70 -20 -20 2x = 50
- 40. Example 2 Find x and the unknown angle. 2x + 20 70° Corresponding 2x + 20 = 70 -20 -20 2x = 50 2 2
- 41. Example 2 Find x and the unknown angle. 2x + 20 Corresponding 70° 2x + 20 = 70 -20 -20 2x = 50 • 2 x = 25
- 42. Example 2 Find x and the unknown angle. 2x + 20 Now we 70° substitute back in. 2(25) + 20 =
- 43. Example 2 Find x and the unknown angle. 2x + 20 Now we substitute 70° back in. 2(25) + 20 = 70 So the missing angle is 70°
- 44. Example 2 Find x and the unknown angle. (3x + 30)° (2x + 40)°
- 45. Example 2 Find x and the unknown angle. (3x + 30)° Find the relationship. (2x + 40)°
- 46. Example 2 Find x and the unknown angle. (3x + 30)° Find the relationship. These angles are supplementary. So (2x + 40)° angle + angle = 180
- 47. Example 2 Find x and the unknown angle. (3x + 30)° Supplementary 3x + 30 (2x + 40)° 2x + 40 = 180
- 48. Example 2 Find x and the unknown angle. (3x + 30)° Supplementary 3x + 30 (2x + 40)° 2x + 40 5x + 70 = 180
- 49. Example 2 Find x and the unknown angle. (3x + 30)° Supplementary 3x + 30 (2x + 40)° 2x + 40 5x + 70 = 180 -70 -70 5x = 110
- 50. Example 2 Find x and the unknown angle. (3x + 30)° Supplementary 3x + 30 2x + 40 5x + 70 = 180 -70 -70 (2x + 40)° 5x = 110 • 5 x = 22
- 51. Example 2 Find x and the unknown angle. (3x + 30)° Supplementary x = 22 Now substitute into angles: (2x + 40)° 3(22) + 30 = 96 2(22) + 40 = 84
- 52. ACTIVITY Green cards: Name the relationship. Write about how you identified the relationship. Use 2-Step Equations to find x and the missing angle. Pink cards: Name the relationship. Write about how you identified the relationship. Use Multi-Step Equations to find x and the missing angles.