Right triangle then with equality only in the isosceles case. If segments of lengths "p" and "q" emanating from vertex "C" trisect the hypotenuse into segments of length "c"/3, then The right triangle is the only triangle having two, rather than one or three, distinct inscribed squares. Let "h" and "k" ("h" > "k") be the sides of the two inscribed squares in a right triangle with hypotenuse "c". Then These sides and the incircle radius "r" are related by a similar formula: The perimeter of a right triangle equals the sum of the radii of the incircle and the three excircles:
Pappus's area theorem rather than only for right angled ones and secondly it uses parallelograms rather than squares. For squares on two sides of an arbitrary triangle it yields a parallelogram of equal area over the third side and if the two sides are the legs of a right angle the parallelogram over the third side will be square as well. For a right-angled triangle, two parallelograms attached to the legs of the right angle yield a rectangle of equal area on the third side and again if the two parallelograms are squares then the rectangle on the third side will be a