2. Geometry Chapter 3 Parallel Lines and Perpendicular Lines Pages 124 - 195

3. 3-1 PAIRS & LINES OF ANGELS What you will learn:  Identify lines and planes  Identify parallel and perpendicular lines  Identify pairs of angles formed by transversals What you will learn:  Identify lines and planes  Identify parallel and perpendicular lines  Identify pairs of angles formed by transversals

4. 3-1 PROPERTIES OF PARALLEL LINES Essential Question: What does it mean when two lines are parallel, intersecting, coincident, or skew? Essential Question: What does it mean when two lines are parallel, intersecting, coincident, or skew?

5. PREVIOUS VOCABULARY  Perpendicular lines

6. CORE VOCABULARY  Parallel Lines  Skew Lines  Parallel Planes  Transversal  Corresponding Angles  Alternate interior Angles  Alternate Exterior Angles  Same-Side (consecutive) interior angles  Parallel Lines  Skew Lines  Parallel Planes  Transversal  Corresponding Angles  Alternate interior Angles  Alternate Exterior Angles  Same-Side (consecutive) interior angles

7. PARALLEL LINES  Two lines that do not intersect  Go in same direction  Coplanar  Two lines that do not intersect  Go in same direction  Coplanar

8. SKEW LINES  Two lines that do not intersect  Are not coplanar  Two lines that do not intersect  Are not coplanar

9. PARALLEL PLANES  Two planes that do not intersect

10. TRANSVERSAL  A line that intersects two or more coplanar parallel lines

11. CORRESPONDING ANGLES  Congruent  Same position  Different location  Congruent  Same position  Different location

12. ALTERNATE INTERIOR ANGLES  Congruent  Inside  Opposites sides  Congruent  Inside  Opposites sides

13. ALTERNATE EXTERIOR ANGLES  Congruent  Outside  Opposites sides  Congruent  Outside  Opposites sides

14. SAME-SIDE (consecutive) INTERIOR ANGLES  Supplementary  Inside  Same side  Supplementary  Inside  Same side

15. PARALLEL LINES  Two coplanar lines that do not intersect

16. STRAIGHT ANGLE  Exactly 180 degrees

17. VERTICAL ANGLES  2 angles directly across from each other  congruent  2 angles directly across from each other  congruent

18. SUPPLEMENTARY ANGLES  Two angles whose measures add up to 180 degrees

19. 3 – 2 PARALLEL LINES & TRANSVERSALS What you will learn:  Use properties of parallel lines  Prove theorems about parallel lines  Solve real-life problems What you will learn:  Use properties of parallel lines  Prove theorems about parallel lines  Solve real-life problems

20. 3-2 PARALLEL LINES & TRANSVERSALS Essential Question:  When two parallel lines are cut by a transversal, which of the resulting pairs of angles are congruent? Essential Question:  When two parallel lines are cut by a transversal, which of the resulting pairs of angles are congruent?

21. CORE VOCABULARY  Transversal  Corresponding Angles  Alternate interior Angles  Alternate Exterior Angles  Same-Side (consecutive) interior angles  Transversal  Corresponding Angles  Alternate interior Angles  Alternate Exterior Angles  Same-Side (consecutive) interior angles

22. TRANSVERSAL  A line that intersects two or more coplanar parallel lines

23. CORRESPONDING ANGLES  Congruent  Same position  Different location  Congruent  Same position  Different location

24. ALTERNATE INTERIOR ANGLES  Congruent  Inside  Opposites sides  Congruent  Inside  Opposites sides

25. ALTERNATE EXTERIOR ANGLES  Congruent  Outside  Opposites sides  Congruent  Outside  Opposites sides

26. SAME-SIDE (consecutive) INTERIOR ANGLES  Supplementary  Inside  Same side  Supplementary  Inside  Same side

27. 3 – 3 Proofs and Parallel Lines What you will learn:  Use the Corresponding Angles Converse  Construct Parallel Lines  Prove theorems about parallel lines  Use Transitive Property of Parallel Lines What you will learn:  Use the Corresponding Angles Converse  Construct Parallel Lines  Prove theorems about parallel lines  Use Transitive Property of Parallel Lines

28. 3 – 3 Proofs and Parallel Lines Essential Question:  Name the two types of pairs of angles that are supplementary Essential Question:  Name the two types of pairs of angles that are supplementary

29. WAYS TO PROVE TWO LINES PARALLEL  Show that a pair of corresponding angles are congruent  Show that a pair of alternate interior or exterior angles are congruent  Show that a pair of same-side interior angles are supplementary  Show that a pair of corresponding angles are congruent  Show that a pair of alternate interior or exterior angles are congruent  Show that a pair of same-side interior angles are supplementary

30. WAYS TO PROVE TWO LINES PARALLEL  Show that both lines are perpendicular to a third line  Show that both lines are parallel to a third line  Show that both lines are perpendicular to a third line  Show that both lines are parallel to a third line

31. Core Concept: Five Types of Angle Pairs  Corresponding ≅  Alternate Interior ≅  Alternate Exterior ≅  Same-Side Interior 180  Vertical ≅  Linear Pair 180  Corresponding ≅  Alternate Interior ≅  Alternate Exterior ≅  Same-Side Interior 180  Vertical ≅  Linear Pair 180

32. PERPENDICULAR LINES  Two lines that intersect to form right angles  If a line is perpendicular to one of two parallel lines, it is also perpendicular to the other line  Two lines that intersect to form right angles  If a line is perpendicular to one of two parallel lines, it is also perpendicular to the other line

33. 3 - 4 PROOFS WITH PERPENDICULAR LINES What you will learn:  Find the distance from a point to a line  Construct Perpendicular lines  Prove theorems about perpendicular lines  Solve real life problems involving perpendicular lines What you will learn:  Find the distance from a point to a line  Construct Perpendicular lines  Prove theorems about perpendicular lines  Solve real life problems involving perpendicular lines

34. 3 – 4 Proofs and Parallel Lines Essential Question:  What conjectures can you make about perpendicular lines? Essential Question:  What conjectures can you make about perpendicular lines?

35. VOCABULARY  Distance from a point to a line  Perpendicular bisector  Distance from a point to a line  Perpendicular bisector

36. Distance from a point to a line  The length of the perpendicular segment from the point to the line

37. Perpendicular Bisector  A perpendicular bisector of a line segment is a line segment that is perpendicular to the segment at its midpoint

38. PARALLEL LINES  Two lines that do not intersect  Go in same direction  If two lines are parallel to the same line, they are parallel to each other  If two lines are perpendicular to the same line, then they are parallel to each other  Two lines that do not intersect  Go in same direction  If two lines are parallel to the same line, they are parallel to each other  If two lines are perpendicular to the same line, then they are parallel to each other

39. TRIANGLE  Three sides  Interior angle sum is 180˚  Symbol: ∆  Sides are called segments  Each point is a vertex  Three sides  Interior angle sum is 180˚  Symbol: ∆  Sides are called segments  Each point is a vertex

40. EQUIANGULAR  All angles are 60˚

41. ACUTE TRIANGLE  Three angles less than 90 degrees

42. RIGHT TRIANGLE  One right angle

43. OBTUSE TRIANGLE  One obtuse angle

44. EQUILATERAL TRIANGLE  All sides congruent

45. ISOSCELES TRIANGLE  At least two congruent sides

46. SCALENE TRIANGLE  No congruent sides

47. EXTERIOR ANGLE  Outside the triangle  Equals the remote interior angles  Supplementary to its adjacent angle  Outside the triangle  Equals the remote interior angles  Supplementary to its adjacent angle

48. REMOTE INTERIOR ANGLES  on the opposite side of the exterior angles  equal the measure of the exterior angle  on the opposite side of the exterior angles  equal the measure of the exterior angle

49. 3 - 5 POLYGON ANGLE- SUM THEOREM STANDARD:  classify polygons  find measures of interior and exterior angles of polygons STANDARD:  classify polygons  find measures of interior and exterior angles of polygons

50. VOCABULARY 1. Polygon 2. Concave Polygon 3. Convex Polygon 4. Diagonal 5. Polygon Angle Sum 6. Polygon Exterior Angle Sum 7. Equilateral Polygon 8. Equiangular Polygon 9. Regular Polygon 1. Polygon 2. Concave Polygon 3. Convex Polygon 4. Diagonal 5. Polygon Angle Sum 6. Polygon Exterior Angle Sum 7. Equilateral Polygon 8. Equiangular Polygon 9. Regular Polygon

51. POLYGON  Closed plane figure  At least 3 sides and angles  Classified by the number of sides  Closed plane figure  At least 3 sides and angles  Classified by the number of sides

52. CONVEX POLYGON  Doesn’t cave in

53. CONCAVE POLYGON  caves in

54. Diagonal  Connects vertices

55. POLYGON ANGLE SUM  (n-2)180

56. POLYGON EXTERIOR ANGLE SUM  The exterior angles of a polygon = 360

57. EQUILATERAL POLYGON  All sides are congruent

58. EQUIANGULAR POLYGON*  All angles are congruent

59. REGULAR POLYGON  Equiangular  Equilateral  Equiangular  Equilateral

60. 3 - 6 LINES IN THE COORDINATE PLANE STANDARD:  graph lines given their equations  to write equations of lines STANDARD:  graph lines given their equations  to write equations of lines

61. VOCABULARY 1. Slope 2. y-intercept 3. x-intercept 4. Graphing Using Intercepts 5. Standard Form 6. Slope Intercept Form 7. Point Slope Form 1. Slope 2. y-intercept 3. x-intercept 4. Graphing Using Intercepts 5. Standard Form 6. Slope Intercept Form 7. Point Slope Form

62. SLOPE

63. y-intercept  Where the graph intersects the y-axis

64. x-intercept  Where the graph intersects the x-axis

65. Graphing Using intercepts  Substitute “0” for x and y to find the intercepts

66. STANDARD FORM  Ax + By = C

67. SLOPE INTERCEPT FORM  y = mx + b  b = y-intercept  m = slope  y = mx + b  b = y-intercept  m = slope

68. POINT SLOPE FORM  y - y 1 = m(x - x 1 )

69. 3 - 7 SLOPES OF PARALLEL AND PERPENDICULAR LINES STANDARD:  relate slope and parallel lines  relate slope and perpendicular lines STANDARD:  relate slope and parallel lines  relate slope and perpendicular lines

70. PARALLEL LINES  Have equal slopes  Two lines that do not intersect  Go in same direction  Have equal slopes  Two lines that do not intersect  Go in same direction

71. PERPENDICULAR LINES  The product of slopes is -1  Two lines that intersect to form right angles  The product of slopes is -1  Two lines that intersect to form right angles

72. SLOPE INTERCEPT FORM  y = mx + b  b = y-intercept  m = slope  y = mx + b  b = y-intercept  m = slope

73. INTERSECT  To cut  Divide by passing through  To cut  Divide by passing through

74. CONGRUENT  equal  The same  equal  The same