1. Look at Figure #1.What is the length of the top? What is the length of the bottom? What is the width of the right side? What is the width of the left side?

2. Is Figure #1 a square?

3. Is Figure #2 exactly the same size and shape as Figure #1?

4. How many triangles are in Figure #1? Do they all have the same measurements? Are they all the same size? Are they all right triangles?

5. How many right triangles are in Figure #2? Are they all the same size as the triangles in Figure #1?

6. If the upper left triangle from each figure were removed, would the areas of the two figures still be equal?

7. If two triangles were removed from each figure, would the remaining areas still be equal?

8. If all of the triangles were removed from each figure, would the remaining areas still be equal?

9. How long is the shortest leg of each triangle? How long is the hypotenuse? How long is the other leg?

10. What are the dimensions of the smaller square in Figure #1? What is its area? Compare that square to one of the triangles; one side of the square is the same length as which leg of the triangle? Compare the length of that leg to the area of the small square.

11. What are the dimensions of the larger square in Figure #1? What is its area? Compare that square to one of the triangles; one side of the square is the same length as which leg of the triangle? Compare the length of that leg to the area of the larger square.

12. What are the dimensions of the large square in Figure #2? What is its area? Compare that square to one of the triangles; one side of the square is the same length as which leg of the triangle? Compare the length of that leg to the area of the large square.

13. If all of the triangles were removed from Figure #1, what would remain?

14. If all of the triangles were removed from Figure #2, what would remain? (8.) If all of the triangles were removed from each figure, would the remaining areas still be equal?

15. If you combined (added) the areas of the small square and the larger square in Figure #1, would that combined area (sum) be equal to the area of the large square in Figure #2?

And a tribute to someone with a brain, who could have used a few extra problems of the week on the Pythagorean Theorem. Ask your students if the diploma helped the scarecrow. Upon receiving his diploma he recited: “The sum of the square roots of any two sides of an isosceles triangle is equal to the square root of the remaining side. Oh, joy, oh, rapture. I’ve got a brain!”

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