Standard formA two-column proof is one method for writing a proof of a theorem in Geometry. Unlike a paragraph form proof, a two-column proof looks organized and easy to read. Statements that lead to a conclusion are listed in the left column and the reasons that support each statement at the left are listed in the right column.The standard form of a two-column proof is shown below. Given: if-part of a theorem Prove: then-part of a theorem Proof:
ExampleTo demonstrate, we will prove the following conditional which deals with an algebraic equation. We will use the Algebraic Properties of Equality in the Reasons column to support the Statements. Conditional: If 5(x+2) = 20, then x = 4.In the conditional above the or the hypothesis if-part is 5(x+2) = 20, the or the conclusion then-part is x = 4. The solution is presented below and a diagram is not necessary in this situation. Given: 5(x+2) = 20 Prove: x = 4 Proof:
In writing two-column proofs, write the statements in a logical manner—present them as if you are leading the reader in a step-by-step process from the to the Given . Write them with clarity and justify each statement with reasons using the Given Information, Postulates, Theorems (previously proven), Definitions of Terms (such as isosceles triangles, angle bisectors, etc), and Algebraic Properties.Prove |