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**RULER POSTULATES & SEGMENT ADDITION**

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

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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.

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**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.

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**NOTATION AB means the line segment with endpoints A and B.**

AB means the distance between A and B. A B AB = 14 cm

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**BETWEEN D G E C 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

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**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.

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**SEGMENT ADDITION POSTULATE**

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 3 PR = 15 P R Q 14 3 Q P 15 R

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**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

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**Q is between R and T. RT = 18 and QR = 10. Find QT.**

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 T 18

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**Find MN if N is between M and P, MN = 3x + 2, NP = 18, and MP = 5x.**

3x = 5x 3x + 20 = 5x -3x x 20 = 2x 10 = x

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1-3: Measuring Segments. Ruler Postulate Every point on a line can be paired with a real number. This makes a ____________ ___________________ between.

1-3: Measuring Segments. Ruler Postulate Every point on a line can be paired with a real number. This makes a ____________ ___________________ between.

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