1. Warm Up Determine whether each statement is true or false. If false, give a counterexample. 1. It two angles are complementary, then they are not congruent. 2. If two angles are congruent to the same angle, then they are congruent to each other. 3. Supplementary angles are congruent. False; only counterexample is 45° and 45° True False; one of many counterexamples would be 60° and 120°

2. Theorem and two-column proof Vocabulary When writing a proof, it is important to justify each logical step with a reason. You can use symbols and abbreviations, but they must be clear enough so that anyone who reads your proof will understand them. Hypothesis Conclusion Definitions Postulates Properties Theorems

3. Given information Def. of Supplementary Angles Substitution Prop of = (Steps 1, 2) Subtraction Prop of =

4. When a justification is based on more than the previous step, you can note this after the reason as in Step 3 of last slide. Helpful Hint

5. Given information Def. of midpoint Given information

6. A theorem is any statement that you can prove. Once you have proven a theorem, you can use it as a reason in later proofs. Key Idea

7. Each page of your proof notebook includes: A title (Theorem 2-6-1 Linear Pair Theorem) Write out the theorem itself Illustrate the theorem Prove the theorem – I will prove this one for you!

8. Linear Pair Theorem (2-6-1) Def of Straight Angle Given Def of Supplementary Angles Angle Addition Postulate Def of Straight Angle If two angles form a linear pair, then they are supplementary. Substitution

9. If two angles are supplementary to the same angle (or to two congruent angles), then the two angles are congruent. Congruent Supplements Theorem (2-6-2)

10. Fill in the blanks to complete a two-column proof of one case of the Congruent Supplements Theorem. Given: Prove: 1a 3b 5c 6d

11. Key Idea Before you start writing a proof, you should plan out your logic. Sometimes you will be given a plan for a more challenging proof. This plan will detail the major steps of the proof for you.

13. Use the given plan to write a two-column proof. Plan: Given: Prove:

14. StatementsReasons 1. 2.2.. 3..3. 4. 5. Given Def. of supp. angles Substitution Def. of supp. angles

15. Use the given plan to write a two-column proof of one case of the Congruent Complements Theorem. Given: Prove: Plan:

16. StatementsReasons 1. 2.2.. 3..3. 4. 5. 6. Substitution Reflex. Prop. of = Subtraction Prop. of = Def. of comp. angles Given

17. Angle Add. Post. Substitution Simplify Division Property of = Lesson Quiz

18. Assignment today is page 113: 1-6 and adding theorems 2- 6-1 through 2-6-4 to your theorem notebook. Remember that homework help is always available at http://www.thinkcentral.com/index.htm http://www.thinkcentral.com/index.htm Today’s keyword is “MG7 2-6”. You need your theorem notebook Monday!