Question

a two-column proof
○ uses a visual representation of the logical flow of steps needed to reach a conclusion.
○ contains a table with a logical series of statements and reasons that reach a conclusion.
○ contains a set of sentences explaining the steps needed to reach a conclusion.
○ uses inductive reasoning to prove a statement.

Explanation:

To determine the correct description of a two - column proof:

1. Analyze the first option: A visual representation of the logical flow of steps is more characteristic of a flow - chart proof, not a two - column proof. So this option is incorrect.
2. Analyze the second option: A two - column proof is structured as a table with two columns. One column contains the statements (the mathematical claims we are making) and the other column contains the reasons (such as definitions, postulates, or previously proven theorems that justify each statement). Through this logical series of statements and reasons, we reach a conclusion. This option accurately describes a two - column proof.
3. Analyze the third option: A two - column proof is not just a set of sentences explaining the steps. It has a specific tabular structure with statements and corresponding reasons. So this option is incorrect.
4. Analyze the fourth option: Two - column proofs typically use deductive reasoning (starting from general principles and deriving specific conclusions) rather than inductive reasoning (which involves generalizing from specific examples). So this option is incorrect.

Answer:

contains a table with a logical series of statements and reasons that reach a conclusion.