Part A The Pythagorean Theorem states that for any given right triangle, a2 + b2 = c2. Using the Pythagorean Theorem, what should be the relationship between the areas of the three squares?

Part B
Using squares 1, 2, and 3, and eight copies of the original triangle, you can create squares 4 and 5. Keep the square 4 and square 5 window open. You will need them to complete the rest of the tasks in this section.

What are the side lengths of square 4 and square 5 in terms of a and b? Do the two squares have the same area?

Part C
Write an expression for the area of square 4 by combining the areas of the four triangles and the two squares.

Part D
Write an expression for the area of square 5 by combining the areas of the four triangles and the one square.

Part E
Since the areas of square 4 and square 5 are the same, set the two expressions equal.

Part F
Which term is on both sides of the equal sign? Since it’s on both sides of the equal sign, you can cancel it out. What is the expression after canceling out the common term?

Part G
What does the equation show after you cancel out a common term?