Relate the Pythagorean Theorem to area by rearranging partitions of a square.
[i]Answer these open ended questions on your own or with others to form deeper math connections.[/i]
When you change the lengths of sides [math]a[/math] and [math]b[/math], what effect does that have on the length of side [math]c[/math]? How are the sizes of the squares with areas [math]a^2[/math], [math]b^2[/math], and [math]c^2[/math] affected?
If you were able to make a right triangle with legs that had lengths of [math]a=5[/math], and [math]b=12[/math], what can you say about the area of a square with side lengths equal to [math]c[/math]?
What is the relationship between the areas of the squares with side lengths [math]a[/math], [math]b[/math], and [math]c[/math]?