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Bell Ringer 11-8 (in your notes) You may use your notes on 2-7 only.

Bell Ringer 11-8 (in your notes) You may use your notes on 2-7 only. What is the title of Lesson 2-7? What is the difference between a postulate and a theorem? Explain the Segment Addition Postulate. What are the Three Properties of Segment Congruence?

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Bell Ringer 11-8 (in your notes) You may use your notes on 2-7 only.

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  1. Bell Ringer 11-8 (in your notes) You may use your notes on 2-7 only. • What is the title of Lesson 2-7? • What is the difference between a postulate and a theorem? • Explain the Segment Addition Postulate. • What are the Three Properties of Segment Congruence? When you are finished, open your book to Lesson 2-7 and take out your notebook if you haven’t already.

  2. Content Standards G.CO.9 Prove theorems about lines and angles. G.CO.12 Make formal geometric constructions with a variety of tools and methods (compass and straightedge, string, reflective devices, paper folding, dynamic geometric software, etc.). Mathematical Practices 2 Reason abstractly and quantitatively. 3 Construct viable arguments and critique the reasoning of others. CCSS

  3. Write proofs involving segment addition. • Write proofs involving segment congruence. Then/Now

  4. Concept

  5. Concept

  6. Proof: Statements Reasons ___ ___ AB  CD 1. 1. Given 2. 2. Definition of congruent segments AB = CD 3. 3. Reflexive Property of Equality BC = BC 4. 4. Segment Addition Postulate AB + BC = AC Use the Segment Addition Postulate Example 1

  7. Proof: Statements Reasons 5. CD + BC = AC 5. Substitution Property of Equality ___ ___ AC  BD 6. 6. Segment Addition Postulate CD + BC = BD 8. 8. Definition of congruent segments 7. 7. Transitive Property of Equality AC = BD Use the Segment Addition Postulate Example 1

  8. Prove the following. Given:AC = ABAB = BXCY = XD Prove:AY = BD Write the given and prove statement above, and then draw the figure. Example 1

  9. Which reason 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 Example 1

  10. A. Addition Property B. Substitution C. Definition of congruent segments D. Segment Addition Postulate Example 1

  11. Concept

  12. Concept

  13. BADGE Jamie is designing a badge for her club. The length of the top edge of the badge is equal to the length of the left edge of the badge. The top edge of the badge is congruent to the right edge of the badge, and the right edge of the badge is congruent to the bottom edge of the badge. Prove that the bottom edge of the badge is congruent to the left edge of the badge. Given: Prove: Proof Using Segment Congruence Example 2

  14. Proof: Statements Reasons 1. Given 1. 2. Definition of congruent segments 2. 3. 3. Given ___ YZ 4. Transitive Property 4. 5. Substitution 5. Proof Using Segment Congruence Example 2

  15. Prove the following. Given: Prove: Example 2

  16. 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. Example 2

  17. A. Substitution B. Symmetric Property C. Segment Addition Postulate D. Reflexive Property Example 2

  18. Class Assignment • p. 147 1, 4

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