Presentation on theme: "RULER POSTULATES & SEGMENT ADDITION"— Presentation transcript:
1 RULER POSTULATES & SEGMENT ADDITION This stuff is AWESOME!
2 POSTULATEA STATEMENT ABOUT GEOMETRIC FIGURES ACCEPTED AS TRUE WITHOUT PROOF.
3 Ruler PostulateThe points on a line can be placed in a one-to-one correspondence with real numbers so thatFor 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 betweenA and B.ABAB = 14 cm
6 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
7 SEGMENT ADDITION POSTULATE If Q is between P and R, then PQ + QR = PR.What does this mean?Start with a picture:PRQIf point Q is between points P and R, then the distance between P and Qplus 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.What does this mean?If the measure of segment PQ plus the measure of segment QR is equal tothe measure of segment PR, then point Q must be between points P and R.123PR = 15PRQ143QP15R
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.PRQ
10 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.L14N12PQ is between R and T. RT = 18 and QR = 10. Find QT.10RQT18
11 Find MN if N is between M and P, MN = 3x + 2, NP = 18, and MP = 5x. 3x = 5x3x + 20 = 5x-3x x20 = 2x10 = x