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 and ∠A ≅ ∠C
Prove: ∠A and ∠C are supplementary

StatementReason
∠A and ∠B are complementaryGiven
m∠A + m∠B = 90°Definition of Complementary Angles
∠A ≅ ∠CGiven
m∠A ≅ m∠CDefinition of Congruent Angles
m∠C + m∠B = 90°Substitution Property of Equality
∠C and ∠B are complementaryDefinition of Complementary Angles

Two Column Proof Example 2:

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

StatementReason
∠1 and ∠2 are right anglesGiven
m∠1 = 90° and m∠2 = 90°Definition of Right Angle
m∠1 = m∠2Transitive Property of Equality
∠1 ≅ ∠2Definition of Congruent Angles

Two Column Proof Example 3:


Given: ABCD is a square
Prove: DBCA

StatementReason
ABCD is a squareGiven
DABCDefinition of Square
DCBADefinition of Square
∠D ≅ ∠BDefinition of Parallelogram
∠ADC ≅ ∠CBASAS Congruence
DBCACPCTC


How does the Two Column Proof Calculator work?

Shows you the details behind a two column proof including the five parts and examples

What 4 concepts are covered in the Two Column Proof Calculator?

given
A thing or set of things helpful in forming a conclusion or judgment
proof
an inferential argument for a mathematical statement, showing that the stated assumptions logically guarantee the conclusion
proposition
a declarative sentence that is either true or false (but not both)
two column proof
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

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