Discovering the Pythagorean Theorem

-Set green leg (side) of the triangle equal to 3. -Set the blue leg(side) of the triangle equal to 4. What is the length of the red side (hypothenuse) of the triangle? What is the area of the green square? What is the area of the blue square? What is the area of the red square?

Keeping the same measures of the triangle as the previous question. Do you find a relationship between the area of the blue triangle, the green triangle and the red triangle?

-Set blue leg (side) of the triangle equal to 5. -Set the green leg(side) of the triangle equal to 12. What is the length of the red side (hypotenuse) of the triangle? What is the area of the green square? What is the area of the blue square? What is the area of the red square?

Keeping the same measures of the triangle as the previous question. Do you find a relationship between the area of the blue triangle, the green triangle and the red triangle?

- Move the green and the blue leg of the triangle to any number you like. What's the length of the green leg of the triangle? What's the length of the blue leg of the triangle? What's the length of the red hypotenuse of the triangle?

On your last triangle, let... a = the blue leg of the triangle b = the green leg of the triangle c = the red hypotenuse of the triangle. Square each of the three numbers. Do you see any relationship between the three squared numbers?

Based on what you have done today... write a rule that has the following pieces...