Course Activity: Explaining the Pythagorean Theorem 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?
Part A
Since triangle 2 is a right triangle, write an equation applying the Pythagorean Theorem to the triangle.
Part B
Since the equations for both triangles have a2 + b2, you can think of the two equations for c2 and n2 as a system of equations. Substitute what a2 + b2 equals in the first equation for a2 + b2 in the second equation. After you substitute, what equation do you get?
Part C
Now, take the square root of both sides of the equation from part B and write the resulting equation.
Part D
Is there any way for this equation to be true? How?
Part E
What does this show about the relationship between the two triangles?
Part F
Does this mean that triangle 1 is a right triangle? Why or why not?
100 POINTS