Question

which are correct statements regarding proofs? select three options.
in a paragraph proof, statements and their justifications are written in sentences in a logical order.
a two - column proof consists of a list statements and the reasons the statements are true.
a flowchart proof gives a visual representation of the sequence of steps without justifications.
a flowchart proof is a visual way of describing the statements and reasons for a proof.
a two - column proof lists only the given information and what is to be proven.

Explanation:

• Paragraph proof: In a paragraph proof, statements and their justifications are indeed written in sentences in a logical order. This is a correct description as it focuses on the narrative - like structure of presenting the proof.
• Two - column proof: A two - column proof consists of a list of statements (in one column) and the reasons (in another column) the statements are true. This is a fundamental characteristic of a two - column proof.
• Flowchart proof: A flowchart proof is a visual way of describing the statements and reasons for a proof. Each step (statement) in the proof is represented as a box, and the arrows between the boxes show the logical flow. The reasons can be written inside the boxes or as labels for the arrows.

Now let's analyze the incorrect options:

• A flowchart proof does have justifications. The steps (statements) in the flowchart are accompanied by the reasons (either in the boxes or as arrow labels), so the statement “A flowchart proof gives a visual representation of the sequence of steps without justifications” is incorrect.
• A two - column proof has more than just the given information and what is to be proven. It has a series of statements and their corresponding reasons. So the statement “A two - column proof lists only the given information and what is to be proven” is incorrect.

Answer:

• In a paragraph proof, statements and their justifications are written in sentences in a logical order.
• A two - column proof consists of a list statements and the reasons the statements are true.
• A flowchart proof is a visual way of describing the statements and reasons for a proof.