The Pythagorean Theorem

I. For this activity you will work with four congruent right triangles and three squares, one for each side of the triangle. Suppose that the triangle sides have length a, b, and c. (The hypotenuse has length c.)

A. Use the four triangles and the two smaller squares
to make a single square.

What is the length of one side of this square?

Record the pattern you use in the square labelled A.

B. Use the four triangles and the largest square
to make a single square.

What is the length of one side of this square? Ans.

Record the pattern you use in the square labelled B.

II. For this activity you will work with two congruent right triangles and the same three squares, one for each side of the triangle.

A. Use two triangles and the two smaller squares to make a single
pentagon.

Record the pattern you use on the pentagon labelled A.

What are the lengths of the sides of the pentagon? Ans.

B. Use two triangles and the largest square to make
a single pentagon.

Record the pattern you use on the pentagon labelled B.

What are the lengths of the sides of the pentagon? Ans.

III. Using either Activity I or II, write an explanation of why this activity shows that the largest square has the same area as the area of the two smaller squares combined.