My favorite theorem is the Pythagoras' theorem. The summary for the theorem is
"The square of the hypotenuse of a right triangle is equal to the sum of of the squares on the two sides."
x = side A y = side B z = hypotenuse
z^2 = x^2 + y^2
This is one of my favorite because it is simple and beautiful. This is one of the earliest theorem that we would learn and it is very important. This theorem is applied virtually everywhere especially in architectures, mechanical designs and etc.