3.2+Puzzling+Through+a+Proof+0910

10-13-09 =FH = =Notes from Class:= The Pythagorean Theorem: a2+b2=c2

Big Idea: The dimensions of a right triangle can be determined with limited information.
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Essential Question: How can I find the perimeter of a right triangle?
=Problem 3.2 Puzzling through a Proof=


 * A) Cut out the puzzle pieces. Examine triangular piece and the three square pieces. How do the side length s of the squares compare to the side lengths of the triangle.**

The side lengths of the two big squares and one of the legs of the triangle are equal. The other leg is much smaller; because of this the area of the square added together equals the hypotenuse. The small square’s side length is 1/6 of the side length of the triangle’s side length.


 * B) Arrange the puzzle pieces to fit exactly into the two puzzle frames. Use four triangles in each frame.**


 * C) Carefully study the arrangements in the two frames. What conclusion can you draw about the relationship among the areas of the three square puzzle pieces?**

I can say that the areas of the two big squares are the same. But the area of the small square is 1/36 of the area of the big squares.


 * D) What does the conclusion you reached in part C mean in terms of the side lengths of the triangles?**

This means the side lengths of the triangle is equal to that of the big squares and like I said before, is 1/6 of the small squares.

Problem 3.2 Follow Up