Triangle the hypotenuse equals the sum of the squares of the lengths of the two other sides. If the hypotenuse has length "c", and the legs have lengths "a" and "b", then the theorem states that The converse is true: if the lengths of the sides of a triangle satisfy the above equation, then the triangle has a right angle opposite side "c". Some other facts about right triangles: For all triangles, angles and sides are related by the law of cosines and law of sines (also called the "cosine rule" and "sine rule"). The triangle inequality states that the sum
Fermat's right triangle theorem and the other is odd. Therefore, both formula_39 and formula_40 are even, one of which is divisible by 4. From these two numbers Fermat derives two more numbers formula_41 and formula_42, one of which is even by the previous sentence. Because formula_43 is a square, formula_44 and formula_45 are the legs of another primitive Pythagorean triangle whose area formula_46. Since formula_27 is itself a square and since formula_48 is even, formula_49 is a square. Thus, any Pythagorean triangle with square area leads to a smaller Pythagorean triangle with square area, completing the proof. Fermat's right triangle theorem Fermat's right triangle