1. 2.5 Vocabulary Two-Column Proof
A proof is deductive reasoning that uses logic, definitions, properties, and previously proven statements to show that a conclusion is true.
When writing a proof, it is important to justify each logical step with a reason. You can use symbols and abbreviations, but they must be clear enough so that anyone who reads your proof will understand them.
Definitions
Postulates
Properties
Theorems
Hypothesis
Conclusion

2. Remember… The Distributive Property: a(b + c) = ab + ac
The Commutative Property: a + b = b + c

3. Remember…
Definitions (Biconditional ↔ )
≅ ↔ =
Mid pt ↔ 2≅
Bis ↔ 2≅
Rt ↔ 90
St ↔ 180 (you can “see” a st )
Acute ↔ 0<A<90
Obtuse ↔ 90<Obtuse<180
Supplementary ↔ 2∡ = 180
Complementary ↔ 2∡ = 90
Postulates:
Seg Addition Postulate
Angle Addition Postulate

4. Example 2. Two Column Proof
Given: A and B are supplementary and mA = 45°
Prove: mB = 135°
STATEMENTS REASONS
1. A and B are supplementary,
mA = 45°
Given
2. mA + mB = 180°
Supplementary ↔ 2∡s = 180
3. 45° + mB = 180°
Subst. Prop of =
Steps 1, 2
4. mB = 135°
Subtr. Prop of =

5. Given: B is the midpoint of AC, AB  EF Prove: BC  EF
Check It Out! Example 3
Given: B is the midpoint of AC, AB  EF
Prove: BC  EF
STATEMENTS REASONS
1. B is the midpoint of AC.
2. AB  BC
3. AB  EF
4. BC  EF

6. Example 4. Given: 1  3 Prove: mDBA = mEBC STATEMENTS REASONS D E2 3 C B A
STATEMENTS REASONS

7. Example 5. Given: M is midpoint of AB Prove: AM = ½ AB
STATEMENTS REASONS