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CHAPTER 2: DEDUCTIVE REASONING

CHAPTER 2: DEDUCTIVE REASONING. Section 2-6: Planning a Proof. PROOFS. All proofs consist of the following 5 pieces: Statement of theorem A diagram illustrating the information Given Prove Statements and Reasons (lead from given to what is to be proved). PREPARING FOR A PROOF.

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CHAPTER 2: DEDUCTIVE REASONING

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  1. CHAPTER 2: DEDUCTIVE REASONING Section 2-6: Planning a Proof

  2. PROOFS All proofs consist of the following 5 pieces: • Statement of theorem • A diagram illustrating the information • Given • Prove • Statements and Reasons (lead from given to what is to be proved)

  3. PREPARING FOR A PROOF • Try to plan your proof before writing steps in the two-column format. • If you do not see a method that works, try reasoning back from what is to be proved. • Study proofs of previous theorems for possible methods.

  4. 1. 1 and 2 are supplementary; 3 and 4 are supplementary. m 1 + m 2 = 180; m 3 + m 4 = 180 m 1 + m 2 = m 3 + m 4 2 ≡ 4, or m 2 = m 4 m 1 = m 3, or 1 ≡ 3 Given Def. of supp. Angles Substitution Prop. Given Subtraction prop. of = PROOF Given: 1 and 2 are supplementary; 3 and 4 are supplementary; 2 ≡ 4 Prove: 1 ≡ 3 1 2 3 4

  5. THEOREM 2-7 Theorem 2-7: If two angles are supplements of congruent angles (or of the same angle), then the two angles are congruent.

  6. THEOREM 2-8 Theorem 2-8: If two angles are complements of congruent angles (or of the same angle), then the two angles are congruent.

  7. a.Name a supplement of angle 2. Name a supplement of angle 3. What justifies your answers to a and b? Angle 1 Angle 4 Angle addition postulate EXAMPLE 1 2 3 4

  8. If 1 and 3 are supplementary, then 1 and ______ are supplementary. If MR = NQ and MP = NP, then ___ = ___. If QRS is a right angle, then 1 and 2 are ____________ ___________ angles. MPQ PR = PQ adjacent complementary EXAMPLE Q M P 1 R 3 2 N S

  9. Vertical angles are _________ congruent. Perpendicular lines _______ form 45 degree angles. A theorem is _______ a true statement. A postulate is ________ used as a reason in a proof. Supplements of congruent angles are ________ congruent. Two angles are ________ complements. A statement in a proof ________ has a reason. always never always sometimes always sometimes always ALWAYS, SOMETIMES, OR NEVER

  10. CLASSWORK/HOMEWORK • Pg. 62, Classroom Exercises 1-6, 8, 10 • Pg. 63, Written Exercises 1-15

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