My question is in the add details box?

Question

What theorem is used in the Isosceles Right Triangle Conjecture and the 30-60-90 Triangle Conjecture? What must you simplify to arrive at a whole or rational number in your answer?

Answer 1

I don't see any other details but maybe I can guess what you are asking. You must assume that the short leg is half the hypotenuse; once you do this you can derive the remaining relationships using the Pythagorian theorem. Hope that was what you were after.