Delving Deeper: Heron Triangles and Moduli Spaces
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We teach triangle congruency every fall, proving and using the big five theorems—SSS, ASA, SAS, AAS, and HL. Preparing to teach this a few years ago, a colleague, Chuck Garabedian, wondered aloud if triangles with the same area and perimeter are congruent. Before you read any further, either prove this or find a counterexample.
Footnotes
Edited by Al Cuoco, acuoco@edc.org Center for Mathematics Education, Education Development Center Newton, MA 02458
E. Paul Goldenberg, pgoldenberg@edc.org Center for Mathematics Education, Education Development Center Newton, MA 02458
Contributor Notes
Steven Rosenberg, sr@math. bu.edu, is a professor in the Department of Mathematics and Statistics, Boston University, Boston MA 02215. His research area is differential geometry, and he works with high school mathematics teachers in the National Science Foundation program Focus on Mathematics.
