Side Lengths of a Right Triangle Reproduced as Perimeters of Other Right Triangles: A Sketch and Proof
In this paper, the author builds upon the work of DiDomenico (1995) and Alsina and Nelson (2011). Given an arbitrary right triangle with side lengths a, b, and c, the author illustrates a method for constructing three smaller right triangles with perimeters a, b, and c. The author also provides a link to a dynamic sketch of the construction that can be used to help students informally explore geometric relationships related to the proof.
DiDomenico, A.S. (citing J. Lawrence) (1995). A property of right triangles. Mathematics Teacher 88(1), 77.
Alsina, C. and Nelsen, R. B. (2011). Icons of mathematics: An exploration of twenty key images. American Mathematical Society (AMS), 82–83.