TY - JOUR AU - Kaufman, Richard PY - 2022/05/20 Y2 - 2024/03/29 TI - Side Lengths of a Right Triangle Reproduced as Perimeters of Other Right Triangles: A Sketch and Proof JF - Ohio Journal of School Mathematics JA - ojsm VL - 90 IS - 1 SE - Articles DO - UR - https://ohiomathjournal.org/index.php/OJSM/article/view/8893 SP - 44--47 AB - <p><span dir="ltr" style="left: 158.779px; top: 365.342px; font-size: 15.9532px; font-family: sans-serif; transform: scaleX(0.925307);" role="presentation">In this paper, the author builds upon the work of DiDomenico (1995) and Alsina and Nelson (2011). </span><span dir="ltr" style="left: 87.4538px; top: 384.486px; font-size: 15.9532px; font-family: sans-serif; transform: scaleX(0.95877);" role="presentation">Given an arbitrary right triangle with side lengths</span> <em><span dir="ltr" style="left: 419.019px; top: 384.486px; font-size: 15.9532px; font-family: sans-serif;" role="presentation">a</span></em><span dir="ltr" style="left: 427.453px; top: 384.486px; font-size: 15.9532px; font-family: sans-serif;" role="presentation">,</span> <em><span dir="ltr" style="left: 435.484px; top: 384.486px; font-size: 15.9532px; font-family: sans-serif;" role="presentation">b</span></em><span dir="ltr" style="left: 442.331px; top: 384.486px; font-size: 15.9532px; font-family: sans-serif; transform: scaleX(0.907238);" role="presentation">, and</span> <em><span dir="ltr" style="left: 478.552px; top: 384.486px; font-size: 15.9532px; font-family: sans-serif;" role="presentation">c</span></em><span dir="ltr" style="left: 485.457px; top: 384.486px; font-size: 15.9532px; font-family: sans-serif; transform: scaleX(0.936121);" role="presentation">, the author illustrates a method for constructing </span><span dir="ltr" style="left: 88.0287px; top: 403.629px; font-size: 15.9532px; font-family: sans-serif; transform: scaleX(0.909959);" role="presentation">three smaller right triangles with perimeters</span> <em><span dir="ltr" style="left: 369.62px; top: 403.629px; font-size: 15.9532px; font-family: sans-serif;" role="presentation">a</span></em><span dir="ltr" style="left: 378.053px; top: 403.629px; font-size: 15.9532px; font-family: sans-serif;" role="presentation">,</span> <em><span dir="ltr" style="left: 385.83px; top: 403.629px; font-size: 15.9532px; font-family: sans-serif;" role="presentation">b</span></em><span dir="ltr" style="left: 392.676px; top: 403.629px; font-size: 15.9532px; font-family: sans-serif; transform: scaleX(0.878979);" role="presentation">, and</span> <em><span dir="ltr" style="left: 427.743px; top: 403.629px; font-size: 15.9532px; font-family: sans-serif;" role="presentation">c</span></em><span dir="ltr" style="left: 434.646px; top: 403.629px; font-size: 15.9532px; font-family: sans-serif; transform: scaleX(0.880602);" role="presentation">. The author also provides a link to a dynamic sketch of the </span><span dir="ltr" style="left: 88.0287px; top: 422.773px; font-size: 15.9532px; font-family: sans-serif; transform: scaleX(0.906481);" role="presentation">construction that can be used to help students informally explore geometric relationships related to the proof.</span></p> ER -