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## Points, Lines, and Planes

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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 . . AB = 12 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 Coordinate Plane Distance Formula • Absolute value of the difference between the coordinates . A . B √**You can only use the word “between” if all three points**are collinear. . . . A B C B is between A and C . E . . D 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. . . . 12 5 C A B 17**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 Coordinate Plane The coordinates of the midpoint of a segment whose endpoints have coordinates a and b is