Presentation on theme: "RULER POSTULATES & SEGMENT ADDITION This stuff is AWESOME!"— Presentation transcript:
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. AB means the distance between A and B. A B AB = 14 cm
C D EG 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: PR 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.
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. PR Q PR Q PR = 15 123 143 15
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. PR Q
N is between L and P. LN = 14 and PN = 12. Find LP. LP N Q is between R and T. RT = 18 and QR = 10. Find QT. RT Q 1412 18 10
Find MN if N is between M and P, MN = 3x + 2, NP = 18, and MP = 5x. MP N 3x + 218 5x 3x + 2 + 18 = 5x 3x + 20 = 5x -3x -3x 20 = 2x 2 2 10 = x MN = 3 (10 ) + 2 MN = 32