TwoColumn Proofs Given 2 x 3 2 3

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

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

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

Two-Column Proofs M Given: m MBA = 84 m ABO = 42 Prove: O B MBO ABO Statements 1. m MBA = 84; m ABO = 42 2. m MBA = m MBO 3. Reasons A 1. Given 2. Angle Addition Postulate m MBA – m ABO = m ABO 3. Subtraction POE 4. 84 – 42 = m ABO 4. Substitution POE 5. 42= m ABO 5. Combine like terms (simplify) 6. m ABO = m MBO 6. If two s have the same measure, then they are equal. 7. ABO MB 0 7. Definition of congruence + m ABO

Two-Column Proofs A M B C N D