Pythagorean Theorem

The following lesson was very successful in introducing and discovering the pythagorean theorem to my students. The developed a table that let students find what the a^2, b^2, c^2 and c, was for each triangle I gave them on a separate sheet(around 8 triangles with different sizes). For instance, the first column listed the number of the triangles referring to the sheet with all the triangles. The second and third column had the literal measurements of side a and side b for each corresponding triangle. The fourth column gave them room to measure the c (hypotenuse) and record it. The fourth and fifth column let them figure out what a^2 and b^2 were. The sixth column was a^2+b^2 (they had to fill it out). The next column was the square root of a^2+b^2 followed by the last column, which was the measurement of the hypotenuse, c (they had to measure it and record it). After the assignment was done, I asked them if they came up with any conclusions and one student said all of the square roots of a^2+b^2 equal c for each triangle. Then I asked them if they can come up with a general formula to figure out what the hypotenuse is if you are given the lengths a and b. After the application, I enforced the Pythgorean Theorem a^2 + b^2= c^2.