1. Chapter 1Section 2 - Ruler Postulate1 Chapter 1 Exploring Geometry: Points, Lines, and Angles in the Plane Section 2 Ruler Postulate Objectives: Students will be able to explain and give examples for the Ruler Postulate, the Ruler Placement Postulate, and the Segment Addition Postulate.

2. Chapter 1Section 2 - Ruler Postulate2 Postulate  A postulate or axiom is an accepted statement of fact. No proof is needed.

3. Chapter 1Section 2 - Ruler Postulate3 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 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.

4. Chapter 1Section 2 - Ruler Postulate4 Example 1 Line Line as a Ruler A B A B 0 1 2 3 4 A corresponds to 0. B corresponds to 3. The distance between A and B is 3. The symbol AB without a bar above the letters, represents the length of AB. AB = |3 – 0| or |0 – 3| = 3

5. Chapter 1Section 2 - Ruler Postulate5 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. A B 0 1 2 3 4 -2-3 5 6 7 A B 0 1 2 3 4 -2-3 5 6 7

6. Chapter 1Section 2 - Ruler Postulate6 Segment Addition Postulate Point B is between points A and C, if and only if A, B, & C are collinear and AB + BC = AC. C A B AC AB BC

7. Chapter 1Section 2 - Ruler Postulate7 Example 2 Prove that B is between A and C. A B 0 1 2 3 4 -2-3 5 6 7 C AB = 5, BC = 3, and AC = 8 AB + BC = 5 + 3 = 8 B is between A and C because 5 + 3 = 8. Also, 3 is between -2 and 6 on the number line.