1. 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

2. 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

3. 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

4. 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

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