Two Column Proof

Two Column Proof Definition:

This consists of a list of statements, and the reasons that we know those statements are true. The two column proof has five parts:
1) Given
2) Proposition
3) Statement Column
4) Reason Column
5) Diagram

Two Column Proof Example 1:

Given: ∠A and ∠B are complementary
∠A ≅ ∠C
Prove: ∠A and ∠C are supplementary

Statement	Reason
∠A and ∠B are complementary	Given
m∠A + m∠B = 90°	Def. of Complementary Angles
∠A ≅ ∠C	Given
m∠A ≅ m∠C	Def. of Congruent Angles
m∠C + m∠B = 90°	Substitution Property of Equality
∠C and ∠B are complementary	Def. of Complementary Angles

Two Column Proof Example 2:

Given: ∠1 and ∠2 are right angles
Prove: ∠1 ≅ ∠2

Statement	Reason
∠1 and ∠2 are right angles	Given
m∠1 = 90° and m∠2 = 90°	Def. of Right Angle
m∠1 = m∠2	Transitive Property of Equality
∠1 ≅ ∠2	Def. of Congruent Angles

Two Column Proof Example 3:

Given: ABCD is a square
Prove: DB ≅ CA

Statement	Reason
ABCD is a square	Given
DA ≅ BC	Def. of Square
DC ≅ BA	Def. of Square
∠D ≅ ∠B	Def. of Parallelogram
∠ADC ≅ ∠CBA	SAS Congruence
DB ≅ CA	CPCTC