If you want to freak out your math professor, tell him/her you know how to draw a triangle with three right angles. But maybe he/she already knows.
How? On the surface of a sphere. Draw a line from anywhere on the equator to one of the poles, next from that pole at a right angle back to the equator, then back to the starting point, forming a 270degree triangle. It's a nonplanar triangle (not drawn on a plane).
A simple trick of a multiplying a twodigit number by 11 often comes in handy. You add the two digits and stick the sum in the middle, but if it's more than 9 you have to carry. So 24 x 11 is 264, but in the case of 78 x 11, since 7+8 is 15, you stick only the five in the middle and carry the 1 (add it to your original 7), making the answer 858. This is not really math taught in school so much as a trick for doing arithmetic in your head, more or less made obsolete by modern calculators.
Another trick like that of my own invention is less often useful but can be impressive. To multiply 19 x 21 in your head, subtract 1 from the square of 20. That 1 is actually the square of the mutual distance from 20. So the answer is 399. For 18 x 22, it's 396 (20 squared minus 2 squared), and so on. For example, 25 x 35 would be 875 (30 squared minus 5 squared), and 15 x 17 is 255.
Not school math, just a little fun.
