Abstract
In “The Surfer Problem: A ‘Whys’ Approach” (Mathematics Teacher 100, no. 1 [August 2006]: 14–19), Larry Copes and Jeremy Kahan introduced a variety of proofs to one of the classic geometry theorems: The sum of distances from all points in the interior of an equilateral triangle to the three edges is the same. The authors went on to prove that this constant distance is the height of the triangle. Although they presented a range of methods for proving this theorem, I offer one additional method that makes use of a lemma concerning isosceles triangles, introduced below. I will then extend the theorem to points in the exterior of the triangle. Finally, I will replace the equilateral triangle with any regular polygon and show that the revised statement is true.
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