Question

Choose the conditional statement that can be used with its converse to form the following biconditional statement: "A triangle is equilateral if and only if its three angles are congruent."
A. If an equilateral triangle has three congruent angles, then it is equilateral.
B. If a triangle has three congruent angles, then it is not equilateral.
C. If the three angles of a triangle are not congruent, then the triangle is not equilateral.
D. If a triangle is equilateral, then its three angles are congruent.

Answer 1

Answer:

D. if a triangle is equilateral then its three angles are congruent

Step-by-step explanation:

Literally, to converse means to switch the hypothesis and conclusion of a conditional statement.

The converse of p → q (if p then q) is is q → p (if q then p)

From the statement "A triangle is equilateral if and only if its three angles are congruent."

The hypothesis is given as

H: A triangle is equilateral

The conclusion is given as

C: its three angles are congruent.

And the condition used is if and only if

Without changing the condition to contra-positive (if not..), the converse statement can be achieved by interchanging the position of the hypothesis and the conclusion.

From option a through d, only option d satisfies this condition.

Answer 2

I think the answer is C.