1. Proving Segment Relationships Postulate 2.8 - The Ruler Postulate The points on any line or line segment can be paired with real numbers so that, given any two points A and B on a line, A corresponds to zero and B corresponds to a positive real number.

2. Proving Segment Relationships Postulate 2.9 – Segment Addition Postulate Given three collinear points A, B, and C, if B is between A and C, then AB + BC = AC. Likewise, if AB + BC = AC, then B is between A and C.

3. Proving Segment Relationships Theorem 2.2 – Segment Congruence Theorem Congruence of segments is reflexive, symmetric, and transitive. Reflexive: segment AB  segment AB Symmetric: If segment AB  segment CD, then segment CD  segment AB. Transitive: If segment AB  segment CD and segment CD  segment EF, then segment AB  segment EF.

4. Example 7-1b Prove the following. Prove: Given:

5. Example 7-1c Proof: Statements Reasons 1. Given 2. Transitive Property 3. Given 4. Addition Property AC = AB, AB = BX AC = BX CY = XD AC + CY = BX + XD 5. Segment Addition Property AC + CY = AY; BX + XD = BD AY = BD 6. Substitution 1. 2. 3. 4. 5. 6.

6. Example 7-2c Prove the following. Prove: Given:

7. Example 7-2d Proof: Statements Reasons 1. Given 2. Transitive Property 3. Given 4. Transitive Property 5. Symmetric Property 1. 2. 3. 4. 5.