A proof of the Pythagorean Theorem
The pattern you discovered yesterday is a theorem in mathematics. A theorem is a general mathematical statement that has been proven true. This theorem is named after the Greek mathematician Pythagoras. The Pythagorean Theorem states a relationship among the lengths of the sides of a right triangle. Today you will explore a geometric proof for this famous theorem.
But first, a little history on Pythagoras
Pythagoras lived in the 500s B.C. He had a devoted group of followers known as the Pythagoreans.
The Pythagoreans were a powerful group. Their influence became so strong that some people feared they threatened the local political structure. They were forced to disband. However, many Pythagoreans continued to meet in secret to teach the ideas of Pythagoras.
The Pythagoreans held Pythagoras in high regard - so high that they gave him credit for all of their discoveries. Much of what we attribute to Pythagoras may actually be the work of one or several of his followers. That includes the Pythagorean Theorem.
Watch the video below for instructions. Then click the link below the video to begin your geometric proof!
Instructions: With your group answer these questions in complete sentences using google document.
1. What conclusion can you draw about the relationship among the areas of the three colored squares a, b, and c?
2. What does the conclusion you reached for #1 mean in terms of the side lengths of the triangles?
3. Compare your results with another group and answer the following: Did that group come to the same conclusion? Is this conclusion true for all triangles? Explain.
4. Suppose a right triangle has legs of length 3 cm and 5 cm. Use your conclusion in #1-3 to find the area of a square drawn on the hypotenuse of the triangle.
5. What is the length of the hypotenuse in #4?
6. State the Pythagorean Theorem as a rule for any right triangle with leg lengths a and b and hypotenuse length c.