Some consequences of the Pythagorean theorem. The converse theorem
Consequence 1: each leg of a right triangle is smaller than the hypotenuse, because a² = c² − b² < c². From this, the shortest distance from a point to a line is the length of the perpendicular: any slanted segment forms a right triangle with the perpendicular and is its hypotenuse. Consequence 2: if the hypotenuse and a leg of one right triangle equal the hypotenuse and a leg of another, the triangles are congruent, since the squares of the other legs are equal. Converse theorem: if in a triangle the square of one side equals the sum of the squares of the other two, the triangle is right. To test, compare the square of the longest side with the sum of the squares of the two shorter sides.
“Corner check”: take three sticks of different lengths, measure them and use the converse theorem to decide in advance whether they make a right angle.