The first one about the machine is a metaphor, because there are no key words such as "like" or "as", so it cant be a simile. And its not comparing anything either, so it cant be an analogy. The second one about the teacher is also a metaphor. The gazelle one is a simile because it has the key word like in it. The triangle one is an analogy, because it is comparing two things. The last one is a simile, because he fought "like" a wild animal.
Hope this helps!