1. Foundations of Geometry
Unit 1
Foundations of Geometry

2. Points, Lines, and Planes
Unit 1: Foundations of Geometry

3. Background
Historically, much of geometry was developed as Euclidean geometry, or non-coordinate geometry. It was named after the Greek mathematician Euclid. Euclid’s most important work was the 13 volumes of The Elements of Geometry. He began his system of geometry with three undefined terms: point, line, and plane. From those terms he defined other geometric vocabulary and postulates. Euclid then proceeded to prove theorems using the definitions and postulates, much as we do today.

4. Geometric Vocabulary
Undefined Terms: These terms can only be explained using examples and descriptions. These undefined terms can be used to define other geometric terms and properties. (The building blocks of geometry.)
Point
Line
Plane

5. Point Description: Naming: Symbolic Representation:
Has no actual size, used to represent an abject or location in space.
Naming:
Named by a capital letter.
Symbolic Representation:

6. Line Description: Naming: Symbolic Representation:
Has no thickness or width, used to represent a continuous set of linear points that extend indefinitely in both directions.
Naming:
Named by a lowercase script letter or by two points on the line.
Symbolic Representation:

7. Plane Description: Naming: Symbolic Representation:
Has no thickness, width, or depth, used to represent a flat surface that extends indefinitely in all directions.
Naming:
Named by a capital script letter or by three non-collinear points in the plane.
Symbolic Representation:

8. Defined Terms
All other terms in geometry must be definable and a definition included a category and then a list of critical attributes.
Example: Space - Set of all points, boundless and three-dimensional.
“Set of all points” – is the classification
“Boundless and three dimensional” – are the critical attributes that make this definition different from other definitions

9. Defined Terms
Space
Set of all points, boundless and three dimensional.

10. Defined Terms Collinear
Set of points, that all lie in the same line. Two points are always collinear. Three points must be checked to determine if they are collinear.

11. Defined Terms Non-collinear
Set of points, that do not all lie on the same line.

12. Defined Terms Coplanar
Set of points, or lines, that lie in the same plane. Three points are always coplanar. Four points must be checked to determine if they are coplanar.

13. Defined Terms Non-Coplanar
Set of points, or lines, that do not lie in the same plane.

14. Defined Terms
Skew Lines
Two non-coplanar lines that do not intersect.

15. Defined Terms Parallel Lines
Two coplanar lines that do not intersect (same slope in y = mx +b form).

16. Defined Terms Perpendicular Lines
Two coplanar lines that intersect at right angles (opposite reciprocal slopes in y = mx + b form).

17. Intersections of geometric terms
Two lines intersect at a
point

18. Intersections of geometric terms
Two planes intersect at a
line

19. Intersections of geometric terms
A line and a plane intersect at a
point

20. Points, Lines, and Planes
Unit 1: Foundations of Geometry

21. Guided Practice

22. Guided Practice

23. Guided Practice

24. Distance and Length
Unit 1: Foundations of Geometry

25. Definitions

26. Examples

27. Ruler Postulate
Points on a line can be paired with real numbers and the distance between the two points can be found by finding the absolute value of the difference between the numbers. Remember, all distance measures must be

28. Examples

29. Ruler Postulate
The Ruler Postulate can also be used to find the coordinate of a segment’s endpoint given the other endpoint and the segment’s length.

30. Examples:

31. Examples:

32. Definitions

33. Guided Practice

34. Guided Practice

35. Constructions

36. Constructions

37. Constructions

38. Constructions

39. Constructions

40. Examples

41. Examples

42. All About Angles
Unit 1: Foundations of Geometry

43. Definitions:

44. Angles can be named by…
the vertex point if there are no other angles that could be confused.
three letters with the vertex as the center and the other letters representing points from each side.
a small number if one is given in the angle.

45. Examples:

46. Examples:

47. Classifying Angles:

48. Examples:

49. Protractor Postulate:

50. Example:

51. Angle Addition Postulate:

52. Examples:

53. Angle Relationships:

54. Angle Relationships:

55. Angle Relationships:

56. Examples:

57. Examples:

58. Angle Constructions

59. Angle Constructions

60. Angle Constructions

61. Angle Constructions

62. Examples

63. Examples

64. True/False and Logic Statements
Unit 1: Foundations of Geometry

65. True/False Summary

66. Examples

67. “And” Statement

68. “And” Statement

69. “Or” Statement

70. “Or” Statement

71. Logic Statement Summary

72. “And” Truth Table

73. “Or” Truth Table

74. On One Condition
Unit 1: Foundations of Geometry

75. Use the following conditional statement in determining your responses: If I get paid today, then I will take you to the movies.

76. Conditional Statements Summary

77. On One Condition

78. On One Condition

79. On One Condition

80. On One Condition

81. On One Condition

82. On One Condition
(They Are Logically Equivalent)