Proof Without Words: A Reciprocal Pythagorean Theorem

by Roger B Nelsen (Lewis and Clark College)

Mathematics Magazine
December, 2009

Subject classification(s): Triangles | Plane Geometry | Geometry and Topology
Applicable Course(s): 4.9 Geometry

The author proves visually that if $a$ and $b$ are the legs and h the altitude to the hypotenuse $c$ of a right triangle, then $(1/a)^2 + (1/b)^2 = (1/h)^2$.

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