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 anglesProve: ∠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 |
How does the Two Column Proof Calculator work?
Free Two Column Proof Calculator - 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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