Fermat's right triangle theorem is, by the Pythagorean theorem, they would form two integer-sided right triangles in which the pair formula_10 gives one leg and the hypotenuse of the smaller triangle and the same pair also forms the two legs of the larger triangle. But if (as Fibonacci asserted) no square congruum can exist, then there can be no two integer right triangles that share two sides in this way. Because the congrua are exactly the numbers that are four times the area of a Pythagorean triangle, and multiplication by four does not change whether a number is square, the existence of a square
Triangle is 1/2, which occurs when , , and the altitude of the triangle from the base of length "a" is equal to "a". The smallest possible ratio of the side of one inscribed square to the side of another in the same non-obtuse triangle is formula_98 Both of these extreme cases occur for the isosceles right triangle. From an interior point in a reference triangle, the nearest points on the three sides serve as the vertices of the pedal triangle of that point. If the interior point is the circumcenter of the reference triangle, the vertices of the pedal triangle