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Two-Column Proofs

Two-Column Proofs. Given: 2x - 3 = 2  3 Prove: x = 11  6. Statements 1. 2x - 3 = 2  3 2. 3(2x - 3) = 2 3. 6x - 9 = 2 4. 6x = 11 5. x = 11  6. Reasons 1. Given 2. Multiplication POE 3. Distributive property 4. Addition POE 5. Division Property. C. B. A. X. m.

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Two-Column Proofs

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  1. Two-Column Proofs Given: 2x - 3 = 23 Prove: x = 116 Statements 1. 2x - 3 = 23 2. 3(2x - 3) = 2 3. 6x - 9 = 2 4. 6x = 11 5. x = 116 Reasons 1. Given 2. Multiplication POE 3. Distributive property 4. Addition POE 5. Division Property

  2. C B A X m Two-Column Proofs Given: A, B, C, X on line m as shownAC = BX Prove: AB = CX Statements 1. A, B, C, X on line m as shown 2. AC = AB + BC 3. BX = BC + CX 4. AC = BX 5. AB + BC = BC + CX 6. AB = CX Reasons 1. Given 2. Segment Addition Postulate 3. Segment Addition Postulate 4. Given 5. Substitution (steps 2, 3, 4) 6. Subtraction POE

  3. C X Y A B Two-Column Proofs Given: AX  BY XC  YC Prove: AC  BC • Reasons • 1. Given • 2. Definition of Congruence • 3. Segment Addition Postulate • 4. Substitution, steps 3 and 4 • 5. Substitution, steps 4 and 5. • 6. Definition of Congruence Statements 1. AX  BY; XC  YC 2. AX = BY; XC = YC 3. AX + XC = AC; BY + YC = BC 4. BY + YC = AC 5. AC = BC 6. AC  BC

  4. Two-Column Proofs M Given: mMBA = 84 mABO = 42 Prove: MBO  ABO O B • Statements • mMBA = 84; mABO = 42 • mMBA = mMBO + mABO • mMBA – mABO = mABO • 84 – 42 = mABO • 42= mABO • mABO = mMBO • ABO  MB0 • Reasons • 1. Given • 2. Angle Addition Postulate • Subtraction POE • Substitution POE • Combine like terms (simplify) • If two s have the same measure, then they are equal. • Definition of congruence A

  5. Two-Column Proofs M A B N C D

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