Goal 1: Use segments postulates Goal 2: Use the distance Formula to measure distances. CAS 1,15,17.

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Presentation transcript:

Goal 1: Use segments postulates Goal 2: Use the distance Formula to measure distances. CAS 1,15,17

Postulates vs. Theorems Postulates (or Axioms) Rules that are accepted. Proving is not necessary Theorems Rules that have to be proven mathematically.

Postulate 1 Ruler Postulate The points on a line can be matched one to one with the real numbers. The real number that corresponds to a point is the coordinate of the point. AB x1x1 x2x2 Names of the points Coordinates of the points

Postulate 1 Ruler Postulate continued- The distance between points A and B, written as AB, is the absolute value of the difference between the coordinates of A and B. AB x1x1 x2x2 AB AB is the length of ( the segment)

A Point "Between" two Points When three points lie on the same line, you can say that one of them is between the other two. AB C D C is between A and B, but D is NOT.

Postulate 2 Segment Addition Postulate If B is between A and C, then AB + BC = AC. If AB + BC =AC, then B is between A and C. ABC

Distance Formula The distance formula is a formula for computing the distance between two points in a coordinate plane. (4, 1) (-4, 3)

Distance Formula If A(x 1, y 1 ) and B(x 2,y 2 ) are points in a coordinate plane, then the distance between A and B is

Example of distance formula Find the distance between (-4, 3) and (4, 1)

Congruent Segments Segments that have the same length. The symbol of congruence is

Congruence vs. Equal Congruence refers to a “thing” that is the same size and shape “is congruent to” Equality refers to the same measure (or distance or length). AB=AD “is equal to”