L 17: Pythagorean Proof

Explain how the following diagram demostrates the Pythagorean Theorem:

Consider the diagram of a square within a square shown below:

Write an expression using the lengths from the diagram for each of the following:

i. Area of the large square in terms of a and b:

ii. Area of the small square:

iii. Total area of the four triangles:

Explain how to use your results from Part A to prove the Pythagorean Theorem:

The Pythagorean Theorem states that if a right triangle has legs of length a and b and hypotenuse of length c, then a squared plus b squared equals c squared. Figures 1 and 2 represent key ideas in proof of the Pythagorean Theorem.

Create and outline a proof for the Pythagorean Theorem based on figure 1 and figure 2, by ordering the following 8 statements into a logical sequence.

1. Start with two large squares with sides of length (a+b)
2. Subdivide the large square in figure 1 into a square with side-lengths a, a square with side-lengths b, and two rectangles with side-lengths a+b.
3. Thus,

4. The total area of the large square in figure 1 is

5. Subdivide the large square in figure 2 into four right triangles with legs a and b and a square in the middle with side-length C.
6. The total area of the large square in Figure 2 is

7. The two large squares have the same area because they are congruent
8. Set the equations equal to each other