Question

test the statement to see if it is reversible. if so, write it as a true biconditional. a triangle has three sides. choose the correct answer below. a. a figure is a triangle if and only if the figure has three sides. b. a figure is a triangle if the figure has three sides. c. the statement is not reversible.

Explanation:

1. First, find the converse of the original statement "A triangle has three sides". The original conditional can be written as "If a figure is a triangle, then it has three sides". The converse is "If a figure has three sides, then it is a triangle".
2. Check if both the original statement and its converse are true. A triangle, by definition, has three sides (original is true). A three - sided figure is a triangle (converse is true).
3. A biconditional statement is of the form "A if and only if B" where both "If A, then B" and "If B, then A" are true. Option A is a biconditional, option B is just the converse (not a biconditional), and option C is incorrect because the statement is reversible.

Answer:

A. A figure is a triangle if and only if the figure has three sides.