Grade School Triangles

Abstract

In grade school, students learn a standard set of Euclidean triangles. Among this set, the usual 45-45-90 and 30-60-90 triangles are the only right triangles with rational angles and side lengths each containing at most one square root. Are there any other such right triangles? We answer this question completely and present an elegant complement called Ailles' rectangle that deserves to be in every geometry teacher's toolkit.

Publisher

Mathematical Association of America

Publication Date

10-1-2010

Publication Title

American Mathematical Monthly

Department

Mathematics

Document Type

Article

DOI

https://dx.doi.org/10.4169/000298910X515749

Keywords

Mathematics

Language

English

Format

text

Link to Full Text

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