Majora's Cat
How about that
They're both ridiculously easy and uninteresting. Now what is interesting is algebraic geometry and analytic geometry, as Kitsu mentioned. I leave you with the topography of a standard 3D object:

Some people can prove triangles congruent all day, but would have a panic attack upon seeing "Factor: 3x^4 + 2x^3 + 3x^3 + 6x^2."
Honestly with how much they tie together you can't really consider them separate entities, so both I guess?
Also, the teachers that say you will use algebra are kind-of right, you can use algebra to help with many mundane tasks and to get the best out of something, but no, you don't need it, then again do you really need to know how to read? I mean it is really helpful no doubt(as is algebra and like all math), but do you really need to know how to read?