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. Chapter 1 Section 2 - Ruler Postulate

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

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

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

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 -3 -2 -1 1 2 3 4 5 6 7 A B -3 -2 -1 1 2 3 4 5 6 7 Chapter 1 Section 2 - Ruler Postulate

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 Chapter 1 Section 2 - Ruler Postulate

Section 2 - Ruler Postulate Example 2 Prove that B is between A and C. A B C -3 -2 -1 1 2 3 4 5 6 7 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. Chapter 1 Section 2 - Ruler Postulate