1. Bell Ringer 11-8 (in your notes) You may use your notes on 2-7 only. 1.What is the title of Lesson 2-7? 2.What is the difference between a postulate and a theorem? 3.Explain the Segment Addition Postulate. 4.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. CCSS 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.

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

4. Concept

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

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

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

9. Example 1 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. ?

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

11. Concept

13. Example 2 Proof Using Segment Congruence 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:

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

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

16. Example 2 Which choice correctly completes the proof? Proof: Statements Reasons 1. Given 1. 2. Transitive Property 2. 3. Given 3. 4. Transitive Property 4. 5. _______________ 5. ?

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

18. Class Assignment p. 147 1, 4