Answer:
Explanation:
The 45-45-90 triangle theorem states that in an isosceles right triangle, the length of the hypotenuse is equal to the square root of 2 times the length of one of the legs. Given triangle DEF is a 45-45-90 triangle, it has two congruent legs, meaning the angles opposite those sides are also congruent. Therefore, we can conclude that each of those angles measures 45 degrees. In a 45-45-90 triangle, the hypotenuse is the side opposite the right angle, which is also the longest side of the triangle. By the Pythagorean theorem, we know that the square of the length of each leg is equal to half the square of the hypotenuse. Since the legs are congruent, we can let one leg be x, then the hypotenuse must be x√2. Therefore, in a 45-45-90 triangle, the length of the hypotenuse is equal to the square root of 2 times the length of one of the legs.