The document discusses three geometric postulates: 1) The ruler postulate establishes a one-to-one correspondence between points on a line and real numbers on the number line, where the distance between points equals the absolute value of the difference of their corresponding numbers. 2) The ruler placement postulate allows choosing a number line such that two given points correspond to 0 and a positive number. 3) The segment addition postulate states that if one point is between two others, the sum of the distances to the end points equals the distance between the outer points.

1. I Can:
explain and give examples for the ruler postulate, the
ruler placement postulate, and the segment addition
postulate.

2. Bell Ringer
 Knowing that AB + BC = AC, solve for AC.
 1. AB = 2, BC = 6 AC = 2 + 6, AC = 8
 2. AB = 1, BC = 4 AC = 1 + 4, AC = 5
 3. AB = 3, BC = 7 AC = 3 + 7, AC = 10
 4. AB = 1, BC = 2 AC = 1 + 2, AC = 3
 5. AB = 5, BC = 1 AC = 5 + 1, AC = 6

3. Rulers
 Measurement is an important part of geometry.
 You use measurement everyday.
 The measuring tool you use most often is a ruler.
 You can think of a ruler as a line with numbers on it.

4. Postulates
 Modern geometry has set some rules on how to use a
ruler for geometric figures.
 The rules are called postulates.
 A postulate is a statement about geometric figures
accepted as true without proof.

5. Absolute Value
 A number’s distance from zero on the number line.

6. Lesson Warm-Up
 Write the absolute value of each number on the
number line.

7. Ruler Postulate:
 The points on a line can be placed in a one-to-one
correspondence with real numbers so that
 1. for every point on the number line, there is exactly
one real number.
 2. for every real number, there is exactly one point on
the line.
 3. the distance between any two points is the absolute
value of the difference of the corresponding real
numbers.

8. Ruler Postulate Example
•A •B
0 5 10
A corresponds to 0.
B corresponds to 3.
The distance between A and B is 3.
Ruler Postulate: AB = 3 – 0 or 0 – 3 = 3

9. 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 a positive
number.

10. Ruler Placement Postulate Example
 Given: A
•A •B
0 5
A= B=
Think about what the ruler placement postulate says we
can do…
0 5

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

12. Segment Addition Postulate
Example
•A •B •C
0 5 10
A= B= C=