<h3>
Answer: D) The triangles are <u>
not</u>
similar</h3>
============================================================
Explanation:
We can immediately rule out choice C because we don't have info about all three pairs of sides. So that's why we can't use the SSS rule.
We may be able to use SAS however. This rule says that if we know a pair of sides are proportional, and if the angles between them are congruent, then we have similar triangles.
However, note the jump from XZ = 2 to XW = 8 is "times 4" while the jump from XY = 3 to XV = 9 is "times 3". The two multipliers don't match up. We would need them to be the same for the sides to be proportional.
Put another way, the equation
8/2 = 9/3
is a false equation
If we tried the equation
8/3 = 9/2
then that's also false. No matter what combos we try, the sides aren't proportional.
So ultimately, we can't use SAS either. This eliminates choice B.
Consequently, it means that we know the triangles aren't similar. If they were similar, then we'd be able to use SAS to prove them to be so.
Therefore, we do have enough information to conclude that the triangles are not similar.
This is why choice D is the final answer.
