Integer triangle rational formula_14 where formula_15 reduces the generated Heronian triangle to its primitive and formula_16 scales up this primitive to the required size. A Pythagorean triangle is right angled and Heronian. Its three integer sides are known as a Pythagorean triple or Pythagorean triplet or Pythagorean triad. All Pythagorean triples formula_17 with hypotenuse formula_18 which are primitive (the sides having no common factor) can be generated by where "m" and "n" are coprime integers and one of them is even with "m" > "n". Every even number greater than 2 can be the leg of a Pythagorean triangle (not necessarily primitive)
Integer triangle or right triangles because all resulting angle combinations generate angles with non-rational sines, giving a non-rational area or side. All isosceles Heronian triangles are decomposable. They are formed by joining two congruent Pythagorean triangles along either of their common legs such that the equal sides of the isosceles triangle are the hypotenuses of the Pythagorean triangles, and the base of the isosceles triangle is twice the other Pythagorean leg. Consequently, every Pythagorean triangle is the building block for two isosceles Heronian triangles since the join can be along either leg. All pairs of isosceles Heronian triangles are given by rational