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.
College Mathematics Journal
School of Mathematics and Statistics

Dlab, V. (Vlastimil), & Williams, K.S. (2019). The Many Sides of the Pythagorean Theorem. College Mathematics Journal, 50(3), 162–172. doi:10.1080/07468342.2019.1580527