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 characteristic of paragraph - style proofs where the flow of reasoning is presented in prose form.
• Two - column proof: A two - column proof consists of a list of statements in one column and the reasons (or justifications) the statements are true in the other column. This is a standard format for two - column proofs.
• 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 arrows show the logical flow from one step to the next, with justifications often included within or near the boxes.

Now let's analyze the incorrect options:

• A flowchart proof does include justifications. The boxes in a flowchart proof typically have the statement and the reason (justification) for that statement. So, the statement “A flowchart proof gives a visual representation of the sequence of steps without justifications” is incorrect.
• A two - column proof lists more than just the given information and what is to be proven. It lists all the statements in the proof process 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.