Presentation on theme: "RULER POSTULATES & SEGMENT ADDITION"— Presentation transcript:
1RULER POSTULATES & SEGMENT ADDITION This stuff is AWESOME!
2POSTULATEA STATEMENT ABOUT GEOMETRIC FIGURES ACCEPTED AS TRUE WITHOUT PROOF.
3Ruler 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.
4Ruler 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.
5NOTATION AB means the line segment with endpoints A and B. AB means the distance betweenA and B.ABAB = 14 cm
6BETWEEN 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
7SEGMENT 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.
8SEGMENT 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
9NOTE 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
10Q 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
11Find MN if N is between M and P, MN = 3x + 2, NP = 18, and MP = 5x. 3x = 5x3x + 20 = 5x-3x x20 = 2x10 = x