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2-7 Proving Segment Relationships

2-7 Proving Segment Relationships. You wrote algebraic and two-column proofs. Write proofs involving segment addition. Write proofs involving segment congruence. Ruler Postulate. You must be able to justify everything you do because you are working in a deductive system.

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2-7 Proving Segment Relationships

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  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. A B C

  5. Page 144 in your book

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

  7. Prove the following. Which reason correctly completes the proof? Proof: Given:AC = ABAB = BXCY = XDProve:AY = BD Statements Reasons 1. 1. Given AC = AB, AB = BX 2. 2. Transitive Property AC = BX CY = XD 3. 3. Given 4. AC + CY = BX + XD 4. Addition Property 5. 5. ________________ ? AC + CY = AY; BX + XD = BD 6. 6. Substitution AY = BD Segment Addition Postulate

  8. Page 145 in your book

  9. Page 146 in your book

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

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

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