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. Set the equations equal to each other

2. The two large squares have the same area because they are congruent
3. The total area of the large square in figure 1 is

4. Thus,

5. The total area of the large square in Figure 2 is

6. 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.
7. Start with two large squares with sides of length (a+b)
8. 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.