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SWLT: Write proofs using geometric theorems and use properties of special pairs of angles. In a proof, you make one statement at a time, until you reach your conclusion. Because the Statements made are based on facts, you are using deductive reasoning. Usually the 1st statementand-reason pair written is the given information Statements Reasons M A Reasons Statements 1. 2. 3. 4. 5. 6. M is a Midpoint of AB AM ≅ MB AM = MB AM + MB = AB AM + AM = AB 2 AM = AB B 1. 2. 3. 4. 5. 6. Given Definition of Midpoint Def. of Congruent Segments Segment Add. Postulate Substitution Prop. Of Eq. Distributive Prop. Of Eq. (Draw two Separate Segments) B A Reasons Statements 1. 2. 3. 4. 5. B is a Midpoint of AC. C is a Midpoint of BD AB ≅ BC BC ≅ CD AB ≅ CD AB = CD C 1. 2. 3. 4. 5. Given Definition of Midpoint Definition of Midpoint Transitive Property Def. of Congruence D Congruent Complements Theorem Congruent Supplements Theorem If two angles are complementary to If two angles are supplementary to the same angle, then they are congruent If m1 + m2 = 90° and m2 + m3 = 90°, then 1 ≅ 3 the same angle, then they are congruent If m4 + m5 = 180° and m5 + m6 = 180°, then 4 ≅ 6 5 3 2 1 4 6 (Congruence of Supplements Proof) 2 1 Reasons Statements 1. 2. 3. 4. 5. 6. 1 & 2 are supplements, 3 & 2 are supplements. m1 + m2 = 180° m3 + m2 = 180° m1 + m2 = m3 + m2 m1 = m3 m1 ≅ m3 3 1. 2. 3. 4. 5. 6. Given Def. of Supplementary Angles Def. of Supplementary Angles Transitive Property Subtraction Property Def. of Congruence