1. 1.3 Segments and Their Measures
Goal 1: Use segments postulates
Goal 2: Use the distance Formula to measure distances.
1.3 Segments and Their Measures
CAS 1,15,17

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

3. 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.
Names of the points A B x1 x2
Coordinates of the points

4. 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.
Demonstrate example 1 pg 17. A AB B x1 x2
AB is the length of ( the segment)

5. 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. D A B C
C is between A and B, but D is NOT.

6. 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. A B C

7. Distance Formula
The distance formula is a formula for computing the distance between two points in a coordinate plane.
(-4, 3)
(4, 1)
Draw picture of the description of the distance formula on the board.

8. Distance Formula
If A(x1, y1) and B(x2,y2) are points in a coordinate plane, then the distance between A and B is
Draw picture on board

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

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

11. Congruence vs. Equal AB=AD “is equal to”
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”