3.1+Discovering+the+Pythagorean+Theorem+0910

12/10/09 SM The side opposite the right angle is called the hypotenuse, and The other two sides that make the right angle are called the legs, The area of the square on the hypotenuse is equal to the sum of the squares on the legs.
 * 3.1, Discovering the Pythagorean Theorem **
 * Essential Question: **How can I find the perimeter of a right triangle?
 * Big Idea:** The dimensions of a right triangle can be obtained with limited information.
 * Notes **
 * 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. **

//√ //** 2 ** || //√ //** 5 ** || //√ //** 8 ** || //√ //**<span style="font-family: "Times New Roman","serif"; font-size: 12pt;">10 ** || //<span style="font-family: "Cambria Math","serif"; font-size: 12pt; line-height: 115%;">√ //**<span style="font-family: "Times New Roman","serif"; font-size: 12pt;"> 13 ** || //<span style="font-family: "Cambria Math","serif"; font-size: 12pt; line-height: 115%;">√ //**<span style="font-family: "Times New Roman","serif"; font-size: 12pt;">18 ** || //<span style="font-family: "Cambria Math","serif"; font-size: 12pt; line-height: 115%;">√ //**<span style="font-family: "Times New Roman","serif"; font-size: 12pt;"> 25=5 ** ||
 * 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)**
 * <span style="font-family: "Times New Roman","serif"; font-size: 12pt;">Length of leg 1 ** ||  ||
 * <span style="font-family: "Times New Roman","serif"; font-size: 12pt;">Length of leg 2 ** ||  ||
 * <span style="font-family: "Times New Roman","serif"; font-size: 12pt;">Area of square on leg 1 ** ||  ||
 * <span style="font-family: "Times New Roman","serif"; font-size: 12pt;">Area of square on leg 2 ** ||  ||
 * <span style="font-family: "Times New Roman","serif"; font-size: 12pt;">Area of square on hypotenuse ** ||  ||
 * <span style="font-family: "Times New Roman","serif"; font-size: 12pt;">Hypotenuse length ** ||
 * <span style="font-family: "Times New Roman","serif"; font-size: 12pt;">Decimal ** ||
 * <span style="font-family: "Times New Roman","serif"; font-size: 12pt;">1 ** ||  ||
 * <span style="font-family: "Times New Roman","serif"; font-size: 12pt;">1 ** ||  ||
 * <span style="font-family: "Times New Roman","serif"; font-size: 12pt;">1 sq u ** ||  ||
 * <span style="font-family: "Times New Roman","serif"; font-size: 12pt;">1 sq u ** ||  ||
 * <span style="font-family: "Times New Roman","serif"; font-size: 12pt;">2 sq u ** ||  ||
 * <span style="font-family: "Times New Roman","serif"; font-size: 12pt;">1 sq u ** ||  ||
 * <span style="font-family: "Times New Roman","serif"; font-size: 12pt;">2 sq u ** ||  ||
 * <span style="font-family: "Times New Roman","serif"; font-size: 12pt;">1.41 ** ||
 * <span style="font-family: "Times New Roman","serif"; font-size: 12pt;">1 ** ||  ||
 * <span style="font-family: "Times New Roman","serif"; font-size: 12pt;">2 ** ||  ||
 * <span style="font-family: "Times New Roman","serif"; font-size: 12pt;">1 sq u ** ||  ||
 * <span style="font-family: "Times New Roman","serif"; font-size: 12pt;">4 sq u ** ||  ||
 * <span style="font-family: "Times New Roman","serif"; font-size: 12pt;">5 sq u ** ||  ||
 * <span style="font-family: "Times New Roman","serif"; font-size: 12pt;">5 sq u ** ||  ||
 * <span style="font-family: "Times New Roman","serif"; font-size: 12pt;">2.24 ** ||
 * <span style="font-family: "Times New Roman","serif"; font-size: 12pt;">2 ** ||  ||
 * <span style="font-family: "Times New Roman","serif"; font-size: 12pt;">2 ** ||  ||
 * <span style="font-family: "Times New Roman","serif"; font-size: 12pt;">4 sq u ** ||  ||
 * <span style="font-family: "Times New Roman","serif"; font-size: 12pt;">4 sq u ** ||  ||
 * <span style="font-family: "Times New Roman","serif"; font-size: 12pt;">8 sq u ** ||  ||
 * <span style="font-family: "Times New Roman","serif"; font-size: 12pt;">8 sq u ** ||  ||
 * <span style="font-family: "Times New Roman","serif"; font-size: 12pt;">2.83 ** ||
 * <span style="font-family: "Times New Roman","serif"; font-size: 12pt;">1 ** ||  ||
 * <span style="font-family: "Times New Roman","serif"; font-size: 12pt;">3 ** ||  ||
 * <span style="font-family: "Times New Roman","serif"; font-size: 12pt;">1 sq u ** ||  ||
 * <span style="font-family: "Times New Roman","serif"; font-size: 12pt;">9 sq u ** ||  ||
 * <span style="font-family: "Times New Roman","serif"; font-size: 12pt;">10 sq u ** ||  ||
 * <span style="font-family: "Times New Roman","serif"; font-size: 12pt;">10 sq u ** ||  ||
 * <span style="font-family: "Times New Roman","serif"; font-size: 12pt;">3.16 ** ||
 * <span style="font-family: "Times New Roman","serif"; font-size: 12pt;">2 ** ||  ||
 * <span style="font-family: "Times New Roman","serif"; font-size: 12pt;">3 ** ||  ||
 * <span style="font-family: "Times New Roman","serif"; font-size: 12pt;">4 sq u ** ||  ||
 * <span style="font-family: "Times New Roman","serif"; font-size: 12pt;">9 sq u ** ||  ||
 * <span style="font-family: "Times New Roman","serif"; font-size: 12pt;">13 sq u ** ||  ||
 * <span style="font-family: "Times New Roman","serif"; font-size: 12pt;">13 sq u ** ||  ||
 * <span style="font-family: "Times New Roman","serif"; font-size: 12pt;">3.61 ** ||
 * <span style="font-family: "Times New Roman","serif"; font-size: 12pt;">3 ** ||  ||
 * <span style="font-family: "Times New Roman","serif"; font-size: 12pt;">3 ** ||  ||
 * <span style="font-family: "Times New Roman","serif"; font-size: 12pt;">9 sq u ** ||  ||
 * <span style="font-family: "Times New Roman","serif"; font-size: 12pt;">9 sq u ** ||  ||
 * <span style="font-family: "Times New Roman","serif"; font-size: 12pt;">18 sq u ** ||  ||
 * <span style="font-family: "Times New Roman","serif"; font-size: 12pt;">18 sq u ** ||  ||
 * <span style="font-family: "Times New Roman","serif"; font-size: 12pt;">4.24 ** ||
 * <span style="font-family: "Times New Roman","serif"; font-size: 12pt;">3 ** ||  ||
 * <span style="font-family: "Times New Roman","serif"; font-size: 12pt;">4 ** ||  ||
 * <span style="font-family: "Times New Roman","serif"; font-size: 12pt;">9 sq u ** ||  ||
 * <span style="font-family: "Times New Roman","serif"; font-size: 12pt;">16 sq u ** ||  ||
 * <span style="font-family: "Times New Roman","serif"; font-size: 12pt;">25 sq u ** ||  ||
 * <span style="font-family: "Times New Roman","serif"; font-size: 12pt;">25 sq u ** ||  ||
 * <span style="font-family: "Times New Roman","serif"; font-size: 12pt;">5.00 ** ||
 * <span style="font-family: "Times New Roman","serif"; font-size: 12pt;">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. **<span style="font-family: "Times New Roman","serif"; font-size: 12pt;">

I noticed that the area of Leg 1 square plus the area of Leg 2 Square is always equal to the area of the hypotenuse square. So my conjecture is Leg 1sq+Leg 2sq=hypotenuse sq

<span style="font-family: "Times New Roman","serif"; font-size: 12pt; line-height: 115%;"> <span style="font-family: "Times New Roman","serif"; font-size: 12pt; line-height: 115%;"> <span style="font-family: "Times New Roman","serif"; font-size: 12pt; line-height: 115%;">If leg 1 is 1unit then its square will be 1u2. If leg 2 is 4units then its square will be 16u2. So the hypotenuse’s square will be 17u2 because 1+16=17. That means its side length will be //<span style="font-family: "Cambria Math","serif"; font-size: 12pt; line-height: 115%;">√17. // <span style="font-family: 'Times New Roman',Times,serif;">**<span style="font-family: "Cambria Math","serif"; font-size: 12pt; line-height: 115%;">F.U ** <span style="font-family: 'Times New Roman',Times,serif;">(Check Table) <span style="font-family: 'Times New Roman',Times,serif;"> <span style="font-family: 'Times New Roman',Times,serif;">(Check Table) <span style="font-family: 'Times New Roman',Times,serif;"> <span style="font-family: "Cambria Math","serif"; font-size: 12pt; line-height: 115%;">
 * 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.**
 * <span style="font-family: 'Times New Roman',Times,serif;">1. Add another to your table. In the column, record the hypotenuse length of each triangle with using the **//<span style="font-family: "Cambria Math","serif"; font-size: 12pt; line-height: 115%;">√ //<span style="font-family: 'Times New Roman',Times,serif;"> **<span style="font-family: 'Times New Roman',Times,serif;">symbol. **
 * <span style="font-family: 'Times New Roman',Times,serif;">2. Approximate each hypotenuse length to the hundredths place. **