Question

I am not sure what the answer should be. Any help?

Answer 1

Answer: Choice D) Not enough information

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Explanation:

We are given that AB is parallel to DC.

This allows us to say that angle BAC = angle DCA because they are alternate interior angles.

We have one pair of congruent angles, but we don't have a second pair of congruent angles. So we cannot use ASA.

We can't use SAS either since we only have information about one pair of congruent sides (AC = AC). We don't know anything about the other sides.

AA is not a congruence theorem. Instead it's a similarity theorem. So we can rule this out as well.

The only thing left is choice D. We don't have enough information. We need to know if AD is parallel to BC, so we can show that angle BCA = angle DAC, which is the other angle pair to use ASA. Or if we knew that AB = CD, then we could use SAS to prove the triangles congruent. Unfortunately we don't have this information.