Proofs without Words in Geometry

Abstract

Pictures and diagrams help high school geometry students develop reasoning and proof-writing skills. P r o o f s w i t h o u t W o r d s S ince the 1970s, the Mathematical Association of America's (MAA) journals Mathematics Magazine and College Mathematics Journal have published "Proofs without Words" (PWWs) (Nelsen 1993). "PWWs are pictures or diagrams that help the reader see why a particular mathematical statement may be true and how one might begin to go about proving it true" (Nelsen 2000, p. i). This article explains how I created and implemented a variation of using diagrams without words to facilitate the development of high school geometry students' reasoning and proof skills. The Common Core (CCSSI 2010) lists approximately twenty geometric theorems for students to prove (e.g., standards G.CO.9, G.CO.10, and G.CO.11) as well as the more general standard of using congruence and similarity criteria for triangles to prove relationships in geometric figures