Students should then do the extension activity for further practice using Geometer's Sketchpad. It is recalled that the name for the longest side is the hypotenuse. Students are informed that there is a concrete relationship between the length of each of the sides and the hypotenuse. This relationship is one of the most famous of mathematical formulas and was discovered in ancient Greece by a man called Pythagoras. Inform them that today we will find out how this relationship was discovered.
Development Have students draw a right triangle and form a square off of each of the three sides.
This is a delicate process and requires a great deal of skill using Geometer's Sketchpad. There is more than one way to do this sketch. A simpler method involves drawing three squares and bringing them together to form a right triangle between them. The drawing of this object will require a lot of one on one help as students will struggle with creating the squares off of each side, especially the hypotenuse since it does not sit perfectly horizontal or vertical. In this exercise the student's familiarity with Geometer's Sketchpad will really become evident as there are several ways to create this drawing and some are quite a bit easier than others.