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Proving Segment Relationships

Learn how to write proofs involving segment addition and segment congruence. This lesson covers the Segment Addition Postulate and provides examples for solving equations and proving statements. Suitable for Standard 4.0 students.

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Proving Segment Relationships

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  1. Proving Segment Relationships

  2. Write proofs involving segment addition. • Write proofs involving segment congruence. Standard 4.0Students prove basic theorems involving congruenceand similarity. (Key) Lesson 7 MI/Vocab

  3. AC A B C 5 8 AB BC Segment Addition Postulate • If B is b/t A and C, then AB + BC = AC. • If AB + BC = AC, then B is b/t A and C. 13 If AB = 5 and BC = 8, then AC = 5 + 8 = 13.

  4. A B C Segment Addition Postulate AB + BC = AC (3x + 2) + (5x – 3) = 15 8x –1 = 15 8x = 16 x = 2 If AB = 3x + 2 BC = 5x – 3 AC = 15 Solve for x.

  5. Prove the following. Given:PR = QS Prove:PQ = RS Proof: Statements Reasons 1. 1. Given PR = QS 2. 2. Subtraction Property PR – QR = QS – QR 3. 3. Segment Addition Postulate PR – QR = PQ; QS – QR = RS 4. 4. Substitution PQ = RS Proof with Segment Addition Lesson 7 Ex1

  6. Prove the following. Given: AC = ABAB = BXCY = XD Prove: AY = BD Lesson 7 CYP1

  7. Which choice correctly completes the proof? Proof: 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 Lesson 7 CYP1

  8. Lesson 7 TH1

  9. Prove the following. Given: Prove: Proof with Segment Congruence Lesson 7 Ex2

  10. Proof: Statements Reasons Proof with Segment Congruence Given: Prove: 1. Given 1. 2. Definition of congruent segments 2. 3. 3. Given 4. Transitive Property 4. 5. Symmetric Property 5. Lesson 7 Ex2

  11. Prove the following. Given: Prove: Lesson 7 CYP2

  12. Which choice correctly completes the proof? Proof: Statements Reasons 1. Given 1. 2. Transitive Property 2. 3. 3. Given 4. Transitive Property 4. ? 5. _______________ 5. Symmetric Property Lesson 7 CYP2

  13. Homework Chapter 2-7 • Pg 121 1 – 3, 16, 19 – 29

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