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RULER POSTULATES & SEGMENT ADDITION

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

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RULER POSTULATES & SEGMENT ADDITION

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  1. RULER POSTULATES & SEGMENT ADDITION This stuff is AWESOME!

  2. POSTULATE • A STATEMENT ABOUT GEOMETRIC FIGURES ACCEPTED AS TRUE WITHOUT PROOF.

  3. 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.

  4. 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.

  5. NOTATION AB means the line segment with endpoints A and B. AB means the distance between A and B. A B AB = 14 cm

  6. BETWEEN D G 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. C

  7. SEGMENT ADDITION POSTULATE If Q is between P and R, then PQ + QR = PR. What does this mean? Start with a picture: P R Q 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.

  8. SEGMENT ADDITION POSTULATE If PQ + QR = PR, then Q is between P and R. Whatdoes 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 3 PR = 15 P R Q 14 3 Q 15 P R

  9. NOTE CARD Segment Addition Postulate #2 If Q is between P and R, then PQ + QR = PR. If PQ + QR = PR, then Q is between P and R. P R Q

  10. N is between L and P. LN = 14 and PN = 12. Find LP. 14 12 L P N Q is between R and T. RT = 18 and QR = 10. Find QT. 10 R T Q 18

  11. Find MN if N is between M and P, MN = 3x + 2, NP = 18, and MP = 5x. 3x + 2 18 M P N 5x MN = 3 (10 ) + 2 MN = 32 3x + 2 + 18 = 5x 3x + 20 = 5x -3x -3x 20 = 2x 2 2 10 = x

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