1. Segments and Their Measures
Chapter 1 Section 1.3
Segments and Their Measures

2. More Definitions Postulate/Axiom Example: The sun rise postulate
Rules that are accepted without proof
Example: The sun rise postulate
Tomorrow the sun will rise in the east.

3. The Ruler Postulate Part 1
The points on a line can be matched one to one with the real numbers.
The real number that corresponds to a point is called the coordinate of the point
Name of points A B x1 x2
Coordinates

4. Ruler Postulate Part 2
The distance between points A and B, is the absolute value of the difference between the coordinates of A and B
The length of is denoted by AB A B x1 x2
AB = |x2 – x1|

5. Ruler Postulate in a nut shell
You can use a ruler to find the coordinates of points on a line.
You can subtract the coordinates of points on a line to find the distance between them.

6. 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 AC A B C AB BC
The whole length is the sum of the little lengths

7. Distance Formula Find AB (AB)2 = (x2 – x1)2 + (y2 – y1)2 •
B (x2, y2)
C(x2, y1) •
A(x1, y1)
|x2 – x1|
|y2 – y1|
Find AB
(AB)2 = (x2 – x1)2 + (y2 – y1)2
This formula can be used to find the distance between any two points in the plane

9. Draw a Sketch of three collinear points then write the segment addition postulate for the points
A is between T and Q T A Q
TA + AQ = TQ H M A
5. M is between H and A
HM + MA = HA S J H
6. J is between S and H
SJ + JH = SH L A B
7. A is between L and B
LA + AB = LB

10. In Exercises 8-11, Use the Following Information. S Is Between T and V
In Exercises 8-11, Use the Following Information. S Is Between T and V. R Is Between S and T. T Is Between R and Q. QV = 18, QT = 6, and TR = RS = SV Q T R S V
8. Find RS
9. Find QS
QV = QT + TR + RS + SV
18 = 6 + RS + RS + RS
12 = 3 RS
4 = RS
QS = QT + TR + RS
QS =
QS = 14

11. In Exercises 8-11, Use the Following Information. S Is Between T and V
In Exercises 8-11, Use the Following Information. S Is Between T and V. R Is Between S and T. T Is Between R and Q. QV = 18, QT = 6, and TR = RS = SV T S V R Q
10. Find TS
11. Find TV
TS = TR + RS
TS = 4 + 4
TS = 8
TV = TR + RS + SV
TV =
TV = 12

12. Suppose J is between H and K, use the segment addition postulate to solve for x then find the length of each segment H J K
HJ = 2x + 4
JK = 3x + 3
KH = 22
HJ + JK = HK
2x x + 3 = 22
5x + 7 = 22
5x = 15
x = 3
HJ = 2(3) + 4 = 10
JK = 3(3) + 3 = 12

13. Suppose J is between H and K, use the segment addition postulate to solve for x then find the length of each segment H J K
HJ = 5x - 3
JK = 8x - 9
KH = 131
HJ + JK = HK
5x x - 9 = 131
13x - 12 = 131
13x = 143
x = 11
HJ = 5(11) – 3 = 52
JK = 8(11) - 9 = 79

14. Find the distance between each pair of points
15. D(1, 3), E(-2, 4), F(0, -4)
Find ED
Find DF
Find EF

15. Find the distance between each pair of points
16. G(-1, 0), H(2, -4), I(1, 3)
Find GH
Find GI
Find HI