1. Some Basic Figures Points, Lines, Planes, and Angles

2. Objectives

16. Definitions and Postulates Geometry

17. Segments, Rays, and Distance 1.Segment- 1.Ray - 1.Opposite Rays- 2.Length of a segment- distance between the two endpoints

18. Vocabulary 1.Congruent- two shapes that have the same size and shape. 2.Congruent Segments-segments that have equal lengths 1.Midpoint of a segment-the point that divides the segment into two congruent segments. 2.Bisector of a segment- a line, segment, ray, or plane that intersects the segment at its midpoint.

19. Postulate 1 (Ruler Postulate) 1.The points on a line can be paired with the real numbers in such a way that any two points can have coordinates 0 and 1 2.Once a coordinate system has been chosen in this way, the distance between any two points equals the absolute value of the difference of their coordinates.

20. Postulate 2 (Segment Addition Postulate) If B is between A and C, then AB + BC = AC A B C

21. Angles Geometru

28. Vocabulary Congruent Angles-angles that have equal measures Adjacent Angles-two angles in a plane that have common vertex and a common side but no common interior points.

29. Vocabulary Bisector of an angle- the ray that divides that angle into two congruent adjacent angle.

34. Postulate 3 (Protractor Postulate)

35. Postulate 4 (Angle Addition Postulate)

36. Postulates and Theorems Relating Points, Lines, and Planes Geometry

37. Postulate 5 A line contains at least two points; a plane contains at least three points not all in one line; space contains at least four points not all in one plane.

38. Postulate 6 Through any two points there is exactly one line.

39. Postulate 7 Through any three points there is at least one plane, and through any three noncollinear points there is exactly one plane.

40. Postulate 8 If two points are in a plane, then the line that contains the points is in that plane.

41. Postulate 9 If two planes intersect, then their intersection is a line.

42. Theorems Theorem 1 If two lines intersect, then they intersect in exactly one point. Theorem 2 Through a line and a point not in the line there is exactly one plane Theorem 3 If two lines intersect, then exactly one plane contains the lines