Pythagorean proof

Task 1

For the first step of this problem, you are given four congruent right triangles that are rotated 90 degrees respectively. Just from looking at the triangles, they are named triangle ABC, where C is the hypotenuse. Go to the first question and then continue the tasks. Then I want you to move all of the triangles so their points touch, making a square in the center, and leaving no open spaces.

Question 1

What is the formula for the outer square?

Now we need the rest of the areas for the inside of the square. What is the area for the inner square?

What about a single triangle?

So what will all four triangles' area be?

Task 2

Knowing all 3 parts, set the whole area equal to the parts of the square and simplify it down.

What is the formula you started with?

What is the formula you end with?

Task 3: test out your formula!

Using your formula you created (c is the hypotenuse), find the missing legs!

Fun fact: this is the pythagorean theorem and this proof came from ancient China over 2,000 (yes, three zeros) years ago!!!!

Why do you think this theorem works? (reflect on your tasks that you just did)