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Warm Up

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.

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Warm Up

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  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. Definitions • Postulates • Properties • Theorems Conclusion Hypothesis Vocabulary Theorem and two-column proof 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.

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

  4. Helpful Hint 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.

  5. Given information Def. of midpoint Given information

  6. Key Idea 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.

  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) If two angles form a linear pair, then they are supplementary. Given Def of Straight Angle Def of Straight Angle Angle Addition Postulate Substitution Def of Supplementary Angles

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

  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.

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

  13. Given Def. of supp.angles Substitution Def. of supp.angles

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

  15. Given Def. of comp. angles Substitution Reflex. Prop. of = Subtraction Prop. of =

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

  17. 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 Today’s keyword is “MG7 2-6”. You need your theorem notebook Monday!

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