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=