Pythagorean Theorem Exploration

Pythagorean Theorem Exploration

1. Draw a table on your paper:

 Length of side Length squared Length of side Length squared Length of Hypotenuse Hypotenuse squared 3 4 6 8 a b c
2. Draw a triangle with sides 6 and 8, like the one shown below. Use a ruler.

1. In the triangle above, x is the hypotenuse. What is x? Use graph paper to measure the hypotenuse and find x. Check your answer with your teacher. Fill in the length in your table.

2. Draw 3 squares on the graph paper, as shown below. Your squares should line up with each side your triangle. Use a ruler. One square will be 6 by 6. One square will be 8 by 8. The third square will be x by x. Check them with the teacher.

3. What are the areas of the squares? Get your answers checked by the teacher.

4. Fill the areas of the squares into your table under “length squared” and “hypotenuse squared”

5. Cut the two smaller squares out of the graph paper. Arrange them so they fit exactly inside the big square. (You may need to cut one of the squares up into pieces to get them to fit, but if you do, only cut along the lines of the graph paper.) What do you notice about the areas of the squares?

6. Now complete the table for a triangle whose sides are a, b, and c. What is the relationship between the squares of the sides (a2, b2, and c2)?