3.1+Discovering+the+Pythagorean+Theorem

= = =October 16, 2008=

Problem 3.1

 * A. Copy the table below. For each row, draw a right triangle with the given lengths on dot paper. Then, draw a square on either side of the triangle. (Table shown below, however we worked on this problem as a class, and so skipped the dot paper figures.**


 * B. For each triangle, find the areas of the squares on the legs and on the hypotenuse. Record your results in the table. (Table shown below)**


 * **Length of leg 1** || **Length of leg 2** || **Area of square on leg 1** || **Area pf square on leg 2** || **Area of square on hypotenuse** ||
 * **1** || **1** || **1 sq u** || **1 sq u** || **2 sq u** ||
 * **1** || **2** || **1 sq u** || **4 sq u** || **5 sq u** ||
 * **2** || **2** || **4 sq u** || **4 sq u** || **8 sq u** ||
 * **1** || **3** || **1 sq u** || **9 sq u** || **10 sq u** ||
 * **2** || **3** || **4 sq u** || **9 sq u** || **13 sq u** ||
 * **3** || **3** || **9 sq u** || **9 sq u** || **18 sq u** ||
 * **3** || **4** || **9 sq u** || **16 sq u** || **25 sq u** ||


 * C. Look for a pattern in the relationship among the areas of the three squares drawn for each triangle. Use the pattern to make a conjecture about the relationship among the areas.**

According to the table's information, the area of the square on the hypotenuse of the triangle is always equal to the sum of the areas on both the legs of the triangle.


 * D. Draw a right triangle with side lengths that are different from those given in the table. Use your triangle to test your conjecture from part C,

** 4 squared + 4 squared should equal x squared Therefore 16 + 16 should equal x squared Therefore length of x = square root 32, which is approximately 5.66

__Follow Up__

Not assigned.