Two Column Proofs
The problem that you just solved could easily be written in the form of a two column proof.
In this method, each step consists of two parts: a statement that is part of the conclusion process, and a geometric fact that supports this statement. The supporting fact could be an undefined term, a theorem, a property, a postulate, or a given fact that is used as a true statement. The statements are listed in the left-hand column and the reasons or evidence are listed in the right-hand column.
Here are some examples of proving a statement in a two-column format. In these problems, all steps necessary in our proofs are supplied along with their supporting reasons.
The first and second examples utilize concepts from Algebra. It will help in the understanding of what each column represents.
Notice that you must always start with the given information.
Example 1:
Given: 9x + 1 = 19
Prove: x = 2
| Statement | Reason |
| 9x + 1 = 19 | Given (because it was given to us already) |
| 9x = 18 | Subtraction Property (because you subtract 1 from each side) |
| x = 2 | Division Property (because you divide by 9 on each side) |
Example 2:
Given: 4(2x+3) = 2(9x-2)
Prove: x = 1.6
| Statement | Reason |
| 4(2x + 3) = 2(9x – 2) | Given |
| 8x + 12 = 18x – 4 | Distributive Property |
| 12 = 10x – 4 | Subtraction Property |
| 16 = 10x | Addition Property |
| 1.6 = x | Division Property |
| x = 1.6 | Symmetric Property |
