Before I start: I taught geometry for a little less than 11 years at the high school level. I have (well, had, it expired two years ago, because I'm not teaching anymore) a Professional Teaching License from the State of Colorado. Pretend this answer is me teaching you.
Let me start off by apologizing: triangle problems suck more, quite possibly than any other type of math problems because they're so unconnected to reality that the parts of our brains that actually do math quite well kinda look at the problem and don't kick in because it doesn't appear to matter.
There are other evil theories you'll have to remember when dealing with hated lines intersecting a pair of parallel lines, but that's another story.
To prove similarity, we need to have SSS, AAA, or SAS.
Oh, and before I go further, this is a terrible problem. For it to work, we have to know that the track in question is running straight (parallel) to the ground, which isn't stated, and we have to know that the little posty things holding up the rail are parallel. If you want me to write a letter to your teacher or principal explaining why this is a terrible problem, let me know. With that, let's solve it.
(If I use a technical math-word and you don't understand what it means, let me know immediately -- math vocab (yeah, I know, the two most evil things in high school) is extremely important for both learning and teaching math. In and of itself, it's completely pointless, but for me to move something from my head to yours, if that something is related to triangles, our sharing a mutual vocabulary is absolutely essential.
Here's a list of the handiest theories you'll use when doing horrible, tedious triangle problems
To prove similarity, we need to have SSS, AAA, or SAS. That is to say, in expanded form "all 3 corresponding sides are proportional," "all 3 corresponding angles are equivalent" or, "a side and its corresponding side are proportional, another side and its corresponding side are proportional, and the proportional angles between them are congruent."
Oh, god. This is such a terrible problem. I'll post a little more when I stop crying. I don't mean "hard" by terrible, I mean terribly written.