Question

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

Explanation:

A two - column proof in mathematics (specifically in geometry or other proof - based subfields) is a structured way of presenting a proof. It contains a table with two columns. One column has a logical series of statements, and the other column has the corresponding reasons (justifications) for each statement. The goal of a two - column proof is to reach a conclusion (usually a theorem or a given - to - be - proven statement).

Looking at the options:

• The first option describes a paragraph proof (a set of sentences explaining steps).
• The second option (the middle one in the right - hand column of the layout) says "contains a table with a logical series of statements and reasons that reach a conclusion", which matches the definition of a two - column proof.
• The third option describes a flow - chart proof (uses a visual representation).
• The left - hand option describes a proof by induction.

Answer:

The middle box in the right - hand group (the one with text "contains a table with a logical series of statements and reasons that reach a conclusion")