Notice how the name of the side corresponds to the angle it is directly across from.
Demonstration of Pythagorean Theorem
Introduction
The Pythagorean theorem states that [math]a^2+b^2=c^2[/math], where [math]a[/math] and [math]b[/math] represent the lengths of the two shorter legs of a right triangle and [math]c[/math] represents the length of the hypotenuse.
Visualization
Warm Up:
Play around with the length of the legs to see how the other sides change. Then, answer the 2 multiple choice questions below.
If [math]a=3[/math] and [math]b=4[/math], then [math]c=?[/math]
If [math]a=5[/math] and [math]c=13[/math] , then [math]b=?[/math]
Making Sense of the Pythagorean Theorem
Relate the Pythagorean Theorem to area by rearranging partitions of a square.
Putting It All Together
[i]Answer these open ended questions with your partner to form deeper math connections.[/i]
Move the pink point at the top of the figure. 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 is the size of the square with area [math]c^2[/math] affected?
Now, move the second point as far over as you can. How are the sizes of the squares with area [math]a^2[/math] and [math]b^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]?
Generalize the relationship between the areas of the squares with side lengths [math]a[/math], [math]b[/math], and [math]c[/math].