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Bell Work: Marsha swam 400 meters in 6 minutes and 12 seconds. Convert that time to minutes.

Bell Work: Marsha swam 400 meters in 6 minutes and 12 seconds. Convert that time to minutes. Answer: 6.2 minutes. Lesson 54: Angle Relationships. Intersecting lines form pairs of adjacent angles and pairs of opposite angles.

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Bell Work: Marsha swam 400 meters in 6 minutes and 12 seconds. Convert that time to minutes.

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  1. Bell Work: Marsha swam 400 meters in 6 minutes and 12 seconds. Convert that time to minutes.

  2. Answer: 6.2 minutes

  3. Lesson 54:Angle Relationships

  4. Intersecting lines form pairs of adjacent angles and pairs of opposite angles.

  5. Adjacent Angles*: share a common vertex and a common side but do not overlap.

  6. Opposite Angles*: are formed by two intersecting lines and share the same vertex but do not share a side.

  7. Opposite angles are also called vertical angles. Vertical angles are congruent.

  8. 1 2 3 4 Adjacent Angles: Opposite Angles: <1 and <3 <1 and <4 <3 and <4 <2 and <3 <4 and <2 <2 and <1

  9. Angles formed by two intersecting lines are related. If we know the measure of one of the angles, then we can find the measure of the other angles.

  10. Two angles whose measures total 180° are called supplementary angles. Supplementary angles may be adjacent angles, but it is not necessary that they are adjacent.

  11. Angle pairs formed by two intersecting lines: Adjacent angles are supplementary Opposite angles (vertical angles) are congruent

  12. 4 3 2 1 40° Example: Refer to this figure to find the measures of angles 1, 2, 3, and 4.

  13. Answer: <1 = 140° <2 = 40° <3 = 50° <4 = 130°

  14. Two angles whose measures total 90° are complementary angles.

  15. Supplementary = 180° Complementary = 90°

  16. Transversal*: a line that intersects one or more other lines in a plane.

  17. If the transversal were perpendicular to the parallel lines, then all angles formed would be right angles.

  18. Corresponding angles: on the same side of the transversal and on the same side of each of the parallel lines. Corresponding angles of parallel lines are congruent.

  19. 1 2 3 4 5 6 7 8 <1 and <5 are corresponding angles and are thus congruent. Name 3 more pairs of corresponding angles.

  20. Answer: <3 and <7 <2 and <6 <4 and <8

  21. Alternate Interior Angles: are on opposite sides of the transversal and between the parallel lines. Alternate interior angles of parallel lines are congruent.

  22. 1 2 3 4 6 7 8 <3 and <6 are alternate interior angles and thus congruent. Name another pair of alternate interior angles.

  23. Answer: <4 and <5

  24. Alternate Exterior Angles: are on opposite sides of the transversal and outside the parallel lines. Alternate exterior angles of parallel lines are congruent.

  25. 1 2 3 4 5 6 7 8 <1 and <8 are alternate exterior angles and thus congruent. Name another pair of alternate exterior angles.

  26. Answer: <2 and <7

  27. Corresponding Angles Same side of transversal, same side of lines Alternate Interior Angles Opposite sides of transversal, between lines Alternate Exterior Angles Opposite sides of transversal, outside of lines

  28. In summary, if parallel lines are cut by a non-perpendicular transversal, the following relationships exist. All the obtuse angles that are formed are congruent All the acute angles that are formed are congruent Any acute angle formed is supplementary to any obtuse angle formed

  29. Turn to page 371 in your books. Begin the practice set problems (a) – (j)

  30. a) Name two pairs of vertical angles

  31. Answer: <a and <c <b and <d

  32. b) Name four pairs of supplementary angles

  33. Answer: <a and <b <b and <c <c and <d <d and <a

  34. c) If m<a is 110 degrees, then what are the measures of angles b, c, and d?

  35. Answer: m<b = 70 degrees m<c = 110 degrees m<d = 70 degrees

  36. d) Which angle is the complement of <g?

  37. Answer: <f

  38. e) Which angle is the supplement of <g?

  39. Answer: <h

  40. f) If m<h is 130 degrees, then what are the measures of <g and <f?

  41. Answer: m<g = 50 degrees m<f = 40 degrees

  42. g) Which angle corresponds to <f?

  43. Answer: <b

  44. h) Name two pairs of alternate interior angles.

  45. Answer: <c and <f <d and <e

  46. i) Name two pairs of alternate exterior angles.

  47. Answer: <a and <h <b and <g

  48. j) If m<a is 105 degrees, what is the measure of <f?

  49. Answer: m<f = 75 degrees

  50. HW: Lesson 54 #1-30

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