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Geom 9point2

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Geom 9point2

1. 1. The Pythagorean Theorem - 9.2 <ul><li>Objectives: </li></ul><ul><li>Prove the Pythagorean Theorem </li></ul><ul><li>Use Pythagorean to solve problems </li></ul>
2. 2. Pythagorean Theorem <ul><li>In a right triangle, the square of the length of the hypotenuse is equal to the sum of the squares of the lengths of the legs. </li></ul><ul><li>c 2 = a 2 + b 2 </li></ul>a b c
3. 3. Proving Pythagorean <ul><li>Look at page 535 </li></ul>
4. 4. Using Pythagorean <ul><li>A Pythagorean triple is a set of 3 positive integers a, b, and c that satisfy the equation c 2 = a 2 + b 2 </li></ul><ul><li>3, 4, and 5 are an example. </li></ul>
5. 5. Using Pythagorean <ul><li>If the legs are 5 and 12, what is the hypotenuse? </li></ul><ul><li>5*5 + 12*12 = 25 + 144 = 169 </li></ul><ul><li>√ 169 = 13 </li></ul><ul><li>5, 12, and 13 are Pythagorean triples. </li></ul>
6. 6. Find the length of the hypotenuse: <ul><li>x 2 = 5 2 + 12 2 </li></ul><ul><li>x = √25 + 144 </li></ul><ul><li>x = 13 </li></ul>x 5 12
7. 7. Find the length of the leg: <ul><li>14 2 = 7 2 + x 2 </li></ul><ul><li>196 = 49 + x 2 </li></ul><ul><li>147 = x 2 </li></ul><ul><li>x = 7√3 </li></ul>14 7 x
8. 8. Find the area of a triangle: <ul><li>Find the height: </li></ul><ul><li>7 2 = 5 2 + h 2 </li></ul><ul><li>49 = 25 + h 2 </li></ul><ul><li>24 = h 2 </li></ul><ul><li>h = √24 </li></ul>7 m 7 m 10 m
9. 9. Find the area of a triangle: <ul><li>Now find the Area: A = 1/2 b*h </li></ul><ul><li>A = 1/2 * 10 * √24 </li></ul><ul><li>A = 24.5 m 2 </li></ul>7 m 7 m 10 m
10. 10. Now do Example 4, p. 537
11. 11. <ul><li>Pythagorean video </li></ul>
12. 12. Homework <ul><li>Do worksheets. </li></ul>