Shortcuts, Do They Work?

Mathematical Practice Standards:  Reason abstractly and quantitatively.  Construct viable arguments and critique the reasoning of others.

Aaron needs to rip (cut length wise) a 2 x 10 into 3 equal strips.  He does not like working with the ugly number that is the width of the 2 x 10, which is 9 ¼”.  Fractions are not his friends and he doesn’t want to divide a fraction by 3 (or any number).  He claims he can pick a number that is easy to divide by three (15, for example) and measure that distance diagonally across the board.  Then mark the board at 5 inch increments (5, 10, and 15”) and his marks will divide the board into equal widths.

Does this method work or is this a shortcut that Aaron has fabricated that is a result of his wishful thinking?

Provide an argument supporting why this works or why it doesn’t’ work.  Use diagrams and words combined with your detailed mathematics to support your argument.

Hint for answer:  Use what you know about congruent triangles.  In this problem, you created 3 of them.