12. The hypotenuse is `c`.

15. It’s a right triangle if the Pythagorean theorem works for its side lengths.

19. (3√5)^{2} ＝ 3^{2} times (√5)^{2}.

31. The area of a triangle is half of its base times its height.

35. Sketch a right triangle where the hypotenuse is from one of the two points to the other.

45. Multiply the numerator and denominator by √3 to make the denominator a whole number.