The Many Sides of the Pythagorean Theorem

Abstract

Summary The Pythagorean theorem gives a fundamental relationship between the lengths of the three sides of a right-angled triangle. We make the case for which theorems of elementary Euclidean geometry should be called the “Pythagorean theorem for an arbitrary triangle” and the “Pythagorean theorem for a quadrilateral.” In making this presentation, we stress the use of the basic properties of triangles over use of the cosine formula.