Question

Which conditional statement has the same truth value as its converse

Answer 1

In other words, you are looking for which one is the biconditional statement. 

A: This is true. Both the Conditional and Converse Statements are true. The Biconditional Statement would be this: The angles are bisected if and only if the angles have two congruent parts. This is true.

B: This is false. It is true as a conditional statement, but if you flip the p and q, it says that ALL acute angles are 60 degrees. This isn't true because a 35 degree angle or a 89 degree angle is also acute.

C: This is False. The conditional statement isn't true. The Converse statement is true but because the conditional statement is not then it is false. You can have two angles the aren't touching and they would be supplementary.

D:  This is False. The Conditional Statement is True but the converse is not. Not all congruent angles are vertical angles. You can have two angles that equal 90 degrees that form a line (supplementary) but they aren't vertical angles.

Therefore, your answer is A.