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Splash Screen. You wrote algebraic and two-column proofs. (Lesson 2–6). Write proofs involving segment addition. Write proofs involving segment congruence. Then/Now. Concept. Concept. Proof:. Statements Reasons. ___. ___. AB  CD. 1. 1. Given. 2.

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  1. Splash Screen

  2. You wrote algebraic and two-column proofs. (Lesson 2–6) • Write proofs involving segment addition. • Write proofs involving segment congruence. Then/Now

  3. Concept

  4. Concept

  5. 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

  6. 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

  7. Prove the following. Given:AC = ABAB = BXCY = XD Prove:AY = BD Example 1

  8. 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

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

  10. Concept

  11. Concept

  12. 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

  13. 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

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

  15. 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

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

  17. End of the Lesson

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