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Points, Lines, and Planes Section 1.2 Segments and Congruence Section 1.3 Use Midpoint and Distance Formulas Ruler Postulate •The points on a line can be matched one to one with the real numbers. •There are an infinite number of points on a line and an infinite number of real numbers. •The real number that corresponds to the point is the coordinate of the point. AB The distance between point A and point B. The length of AB. A B . . 12 AB = 12 •AB means “the distance between point A and Point B”. (number) •AB means “line AB”. (figure) •AB means “segment AB”. (figure) •AB means “ray AB”. (figure) Distance Formulas Number Line • Absolute value of the difference between the coordinates A . Coordinate Plane • Distance Formula B . √ You can only use the word “between” if all three points are collinear. . A . . B C B is between A and C . D .E . F E is not between D and F Segment Addition Postulate If B is between A and C, then AB + BC = AC. If AB + BC = AC, then B is between A and C. . A 5 . 12 B 17 .C Congruent Segments Line segments that are the same length. AB = CD The lengths are equal. The Segments are congruent. .A .B .C .D Midpoint The point that divides the segment into two congruent segments. A segment has exactly one midpoint. .A .M .B M is the midpoint of AB. Segment Bisector •A point, ray, line, line segment , or plane that intersects a segment at its midpoint. •A segment can have an infinite number of bisectors. . . . Midpoint Formula Number Line The coordinates of the midpoint of a segment whose endpoints have coordinates a and b is Coordinate Plane