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RULER POSTULATES & SEGMENT ADDITION This stuff is AWESOME! POSTULATE • A STATEMENT ABOUT GEOMETRIC FIGURES ACCEPTED AS TRUE WITHOUT PROOF. Ruler Postulate • The points on a line can be placed in a one-to-one correspondence with real numbers so that – For every point on the line, there is exactly one real number. – For every real number, there is exactly one point on the line. – The distance between any two points is the absolute value of the difference of the corresponding real numbers. Ruler Placement Postulate • Given two points, A and B on a line, the number line can be chosen so that A is at zero and B is at a positive number. AB means the line segment with endpoints A and B. A B AB means the distance between A and B. AB = 14 cm D G C E E is between C and D. G is not between C and D. For one point to be between two other points, the three points must be collinear. If Q is between P and R, then PQ + QR = PR. What does this mean? Start with a picture: P Q R If point Q is between points P and R, then the distance between P and Q plus the distance between Q and R is equal to the distance between P and R. If PQ + QR = PR, then Q is between P and R. What does this mean? If the measure of segment PQ plus the measure of segment QR is equal to the measure of segment PR, then point Q must be between points P and R. 12 P 3 PR = 15 R Q 14 P Q 15 3 R NOTE CARD Segment Addition Postulate #2 If Q is between P and R, then PQ + QR = PR. P Q R If PQ + QR = PR, then Q is between P and R. N is between L and P. LN = 14 and PN = 12. Find LP. L 14 N 12 P Q is between R and T. RT = 18 and QR = 10. Find QT. 10 R Q 18 T Find MN if N is between M and P, MN = 3x + 2, NP = 18, and MP = 5x. M 3x + 2 N 18 P 5x 3x + 2 + 18 = 5x 3x + 20 = 5x -3x -3x 20 = 2x 2 2 10 = x MN = 3 (10 ) + 2 MN = 32