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 of a right triangle with square area. By dividing by any common factors, one can assume that this triangle is primitive and from the known form of all primitive Pythagorean triples, one can set formula_23, formula_24, and formula_25, by which the problem is transformed into finding relatively prime integers formula_26 and formula_27 (one of which is even) such that formula_28 is square. The four linear factors formula_26, formula_27, formula_31, and formula_32 are relatively prime and therefore must themselves be squares; let formula_33 and formula_34. Both formula_35 and formula_36 must be odd since exactly one of formula_26 or formula_27 is even