Answer: choices B, C, D and E
B) triangle RSP is similar to triangle ZXY
C) triangle SRP is similar to triangle XZY
D) triangle PSR is similar to triangle YXZ
E) triangle RPS is similar to triangle ZYX
In short, the answers is nearly everything but the first and last answer choice
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For the first triangle, angle S is 54 degrees. In the other triangle, angle X is also 54 degrees. This means that the two angles correspond as they are equal to one another. The answer will have the letters S and X show up in the same position, whether that position is the first, second or third place of the three letter sequence.
Choice A is not one of the answers. RPS ~ XYZ is false because of what I mentioned above. We see that S is shown last in RPS while X is shown first in XYZ. The letters S and X do not correspond together, so we can cross choice A off the list.
Choice B is one of the answers because we have R corresponding to Z (first letters of each sequence RSP and ZXY; both are 41 degrees) and we have S correspond to X, and we have P correspond to Y (both the same measure as well)
Choice C is another answer for similar reasons as choice B. The only difference is that R and S have swapped, so have X and Z. The order is important or else things wouldn't line up properly.
Choice D is another answer. Again we have the same correspondence of P to Y (both in the first slot), S to X (second slot), and R to Z (third slot). For each slot, the pair of angles are both the same measure.
Choice E is another answer. Similar reasons as before, just a different order.
Choice F is not one of the answers. We see that P and Z occupy the second slots, but they aren't congruent angles.
