How to Write a 2-Column Proof
A 2-column proof is a mathematical proof that is presented in a two-column format. The left column contains the statements of the proof, while the right column contains the reasons for each statement. 2-column proofs are commonly used in geometry and other branches of mathematics.
Step-by-Step Instructions
- Understand the theorem or proposition that you are proving. Make sure that you know what the theorem or proposition is stating and what it means.
- Write the given information in the left column. The given information includes any facts or assumptions that you are starting with.
- Write a statement in the left column that follows logically from the given information. The statement should be related to the theorem or proposition that you are proving.
- Write the reason for the statement in the right column. The reason should be a logical explanation of why the statement is true.
- Repeat steps 3 and 4 until you have proven the theorem or proposition. The last statement in the left column should be the theorem or proposition that you are proving.
Example
Here is an example of a 2-column proof that proves the Pythagorean theorem.
| Statement | Reason |
|---|---|
| The triangle is a right triangle. | Given |
| Let a be the length of the side opposite the right angle. | Definition of a right triangle |
| Let b be the length of the side adjacent to the right angle. | Definition of a right triangle |
| Let c be the length of the hypotenuse. | Definition of a right triangle |
| a2 + b2 = c2 | Pythagorean theorem |
Best Practices
- Use clear and concise language. The statements and reasons in your proof should be easy to understand.
- Be logical. Each statement in your proof should follow logically from the previous statement.
- Use proper grammar and punctuation. Your proof should be well-written and free of errors.
- Proofread your work. Make sure that your proof is accurate and complete before submitting it.
Conclusion
Writing a 2-column proof is a valuable skill that can be used to prove mathematical theorems and propositions. By following the steps and best practices outlined in this article, you can write clear, concise, and logical proofs.
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