## Wednesday, October 6, 2010

### Pythagorean Puzzler

Today my students are investigating the Pythagorean triangle relationships.  The first question is can we tell the angle type of a triangle just by the side lengths?  (A previous post shares that investigation.)  Then they'll look at problems using the Pythagorean Theorem (same post - it was a long one!).  Finally, they'll look at developing some reasons that the theorem is true.  One visual geogebra proof is here - that's the easiest to extend to an algebraic proof.  But my favorite visual is the puzzle proof, where the medium square is cut up to make the square on the hypotenuse with the smallest square.  Here's the sketch to explore that:

Sorry, the GeoGebra Applet could not be started. Please make sure that Java 1.4.2 (or later) is installed and active in your browser (Click here to install Java now)

I was going for a feltboard look - what do you think?  It's also available as a standalone webpage or the original Geogebra file.

My notes on embedding geogebra in a webpage are here, based on Kate Nowak's instructions.