Why would my teacher give me a math paper on something I didn't learn yet? Is she okay?

your teacher is crazy about she think you are smart

To see what you know, which is used to find out what you need to learn.

check the picture below.

well, the angle at the vertex d is clearly not a right-angle, let's check for the one at the vertex f which does look like,   however if it's indeed, that means ef is perpendicular to df, in which case their slopes will be negative reciprocal of each other.

so the negative reciprocal of the slope of ef is 1, however the slope of df is not 1, is 1/2, so nope, they're not perpendicular lines.

the circle one