Jim Smith JCHS Section 7-2 spi.3.2.N

If You Have A Right Triangle, Then a² + b² = c² a b c

Find The Value Of X x x 2 x 6

x 3 5 x² + 3² = 5² x ² + 9 = 25 x² = 16 x = 4 This is our 1 st special right Triangle 3,4,5

7 8 x 7² + 8² = x² = x² 113 = x² 113 = x 113 = x 10.6 = x Find The Value Of X

2 x 6 2² + x² = 6² 4 + x² = 36 x² = 32 x² = 32 x = 32 = 4 2 x = 32 = 4 2 x = 5.7 x = 5.7

The Converse Of The Pythagorean Theorem If a² + b² = c², Then You Have A Right Triangle

Do These Lengths Form Right Triangles ? 5, 6, 10 6, 8, 10 5² + 6² ?? 10² ≠ ≠ 100 NO NO 6² + 8² ?? 10² = = 100 YES YES

If the c² = a² + b², then right If the c² is greater, then obtuse If the c² is smaller, then acute What Kind Of Triangle ? a² + b² ?? c² a² + b² ?? c²

4,7,9 4,7,9 4² + 7² ?? 9² ?? OBTUSE OBTUSE greater

5,5,7 5² + 5² ?? 7² ?? ?? ?? 49 ACUTE ACUTE SMALLER

A Pythagorean Triple Is Any 3 Integers That Form A Right Triangle 3, 4, 5 Family6,8,1030,40,5015,20,25 5, 12, 13 Family10,24,2625,60,6535,84,91