1. 2-7 Proving Segment Relationships You wrote algebraic and two-column proofs. Write proofs involving segment addition. Write proofs involving segment congruence.

2. Ruler Postulate You must be able to justify everything you do because you are working in a deductive system.

3. Page 144 in your book

4. Segment-Addition Postulate You need to be able to add the lengths of adjacent segments to find the length of longer segments. Point B is between points A and C if and only if A,B, and C are collinear and AB + BC = AC. AB C

5. Page 144 in your book

6. 2. Definition of congruent segments AB = CD 2. 3. Reflexive Property of Equality BC = BC 3. 4. Segment Addition Postulate AB + BC = AC 4. StatementsReasons 1. 1. Given AB  CD ___ 6. Segment Addition Postulate CD + BC = BD 6. 7. Transitive Property of Equality AC = BD 7. 5. Substitution Property of Equality 5. CD + BC = AC 8. Definition of congruent segments 8. AC  BD ___

7. Prove the following. Given:AC = AB AB = BX CY = XD Prove:AY = BD 1. Given AC = AB, AB = BX 1. 2. Transitive Property AC = BX 2. 3. Given CY = XD 3. 4. Addition PropertyAC + CY = BX + XD4. AY = BD 6. Substitution6. Proof: StatementsReasons Which reason correctly completes the proof? 5. ________________ AC + CY = AY; BX + XD = BD 5. ? Segment Addition Postulate

8. Page 145 in your book

9. Page 146 in your book

10. Prove the following. Given: Prove: Proof: Statements Reasons 1. Given 1. 2. Transitive Property 2. 3. Given 3. 4. Transitive Property 4. 5. _______________ 5. ? Symmetric Property

11. Assignment Page 147, 1, 2 4, 9, 11