Two-Column Proofs Given: 2x - 3 = 23 Prove: x = 116 Statements

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Presentation transcript:

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

Two-Column Proofs Given: A, B, C, X on line m as shown AC = BX Prove: AB = CX A B C X m 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

Two-Column Proofs C A B X Y Given: AX  BY XC  YC Prove: AC  BC 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 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

Two-Column Proofs M O B A 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

Two-Column Proofs A M B C N D