Which statement is the if/then conditional statement of the following? Vertical angles are congruent.

A. If two angles are vertical angles, then they are congruent.

B. If two angles are congruent, then they are vertical angles.

C. If two angles are not congruent, then they are not vertical angles.

D. If two angles are not vertical angles, then they are not congruent.

Question

Mathematics

Beau Chapman

12 February, 01:38

Which statement is the if/then conditional statement of the following? Vertical angles are congruent.

A. If two angles are vertical angles, then they are congruent.

B. If two angles are congruent, then they are vertical angles.

C. If two angles are not congruent, then they are not vertical angles.

D. If two angles are not vertical angles, then they are not congruent.

+2

Answers (1)

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Skylar Mason · Answer 1

An if-then statement must hold under any condition. Let's take it case by case:

A. This one makes sense, and is perfect! If two angles are vertical, then they must be congruent. This holds no matter what. This is your answer.

B. This doesn't hold because Alternate Interior Angles can also be congruent (along with many others). Two angles don't have to be vertical to be congruent.

C. This one is also true because this is the contrapositive of Option A. (Read my reasoning on D to know what a contrapositive is). Therefore, this is correct.

D. This one is the contrapositive of B, which makes it the exact same as B. Thus, this is not the answer. Contrapositive, by the way, just means that it's the inverse and opposite of a given statement. Let's say P is the contrapositive of Q. If this is the case, then if Q is true, P must be true. In our case, Option D is the contrapositive of Option B and since Option B is not true, neither is D.