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Pythagorean Theorem 1. Turn your graph paper sideways or landscape. Draw a large square on the left hand side of the paper, taking up about half of your graph paper. 2. Label the left side as length “a”. a Pythagorean Theorem 3. Starting at the bottom right hand side of the square, label a point that is greater than halfway up the side. 4. This is the length of your second square. Using that as one side, draw a second square adjacent to the first square. 5. Label the right side as length “b” a b Pythagorean Theorem 6. Along the bottom of the first square, mark off the distance that is the length of the smaller square. Label that length as “b”. a b b Pythagorean Theorem 7. Draw a segment connecting your point to the upper left hand corner of the large square. 8. Label BOTH sides of that segment as length “c”. a c c b b Pythagorean Theorem 9. Draw another segment that connects the point to the upper right hand corner of the small square. 10. Notice the right triangle in the large square with sides a, b, and c. a c c b b Pythagorean Theorem 11. You now have five different pieces. a c c b b Pythagorean Theorem 12. Using your scissors, cut out each piece formed. a c c b b Pythagorean Theorem 13. Rearrange the pieces to make a single large square with sides of length “c”. c a c b b Pythagorean Theorem c c Pythagorean Theorem By rearranging the pieces to make a single large square with sides of length “c”, what does this mean? + Area of square “a” a 2 Area of square “b” = = a b 2 Area of square “c” c c b 2 c Pythagorean Theorem Therefore, a b c 2 2 2