Question

I put D since I believe HL applies here but am not sure. Could anybody please help?

Answer 1

Answer:  B) II and III

====================================================

Explanation:

Check out the diagram below.

On the left side shows ASA can be used to prove the triangles congruent. Note the color coding to see how the angles match up. Also note that the segment TR is between angles STR and SRT. The order is important because ASA is different from AAS.

Angle STR = Angle VTU because they are vertical angles

Angle SRT = Angle VUT since they are alternate interior angles. Note how SR is parallel to UV. If the lines weren't parallel, then the alternate interior angles would not be congruent.

We can use AAS because if we know two angles of a triangle, we can find the third angle. Despite the fact that something like RST looks like a right angle, we don't have enough info to say it is or not. The square angle marker is missing. So it could be 90 degrees, or it might be something like 89 degrees instead. We don't have enough info. So we cannot use HL.

AAA or AA is not a congruence theorem. It's a similarity theorem. So we cross this off the list.