7 2 pyth theorem

Jim Smith JCHSJim Smith JCHSSection 7-2 spi.3.2.NSection 7-2 spi.3.2.N

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If You Have A Right Triangle,If You Have A Right Triangle,Then aThen a² + b² = c²² + b² = c²

aa

bb

cc

Find The Value Of XFind The Value Of X

xx

33

55 77

88

xx22

xx

66

Find The Value Of XFind The Value Of X

xx

33

55x² + 3² = 5² x² + 3² = 5² xx² + 9 = 25² + 9 = 25x² = 16x² = 16x = 4x = 4

This is our 1This is our 1stst special right special right

Triangle Triangle 3,4,53,4,5

77

88

xx7² + 8² = x²7² + 8² = x²49 + 64 = x²49 + 64 = x²113 = x²113 = x² 113 = x113 = x10.6 = x 10.6 = x

Find The Value Of XFind The Value Of X

Find The Value Of XFind The Value Of X

22

xx

662² + x² = 6²2² + x² = 6²4 + x² = 364 + x² = 36 x² = 32x² = 32 x = 32 = 4 2x = 32 = 4 2 x = 5.7 x = 5.7

The Converse Of The The Converse Of The Pythagorean TheoremPythagorean Theorem

If a² + b² = c², Then If a² + b² = c², Then YouYou

Have A Right TriangleHave A Right Triangle

Do These Lengths Form Do These Lengths Form Right Triangles ?Right Triangles ?

5, 6, 10 6, 8, 105, 6, 10 6, 8, 105² + 6² ?? 10²5² + 6² ?? 10²25 + 36 10025 + 36 100

61 61 ≠ ≠ 100 100 NONO

6² + 8² ?? 10²6² + 8² ?? 10²36 + 64 10036 + 64 100

100 100 = = 100 100 YESYES

If the If the c²c² = a² + b² , then = a² + b² , then rightright

If the If the c²c² is is greatergreater, then , then obtuseobtuse

If the If the c²c² is is smallersmaller, then , then acuteacute

What Kind Of Triangle ? What Kind Of Triangle ? a² + b² ?? a² + b² ?? c²c²

4,7,94,7,94² + 7² ?? 9²4² + 7² ?? 9²16 + 49 ?? 8116 + 49 ?? 81 65 8165 81

OBTUSEOBTUSE

greatergreater

5,5,75,5,75² + 5² ?? 7² 5² + 5² ?? 7² 25 +25 ?? 4925 +25 ?? 49 50 ?? 4950 ?? 49

ACUTEACUTE

SMALLERSMALLER

A Pythagorean Triple Is Any 3 A Pythagorean Triple Is Any 3 Integers That Form Integers That Form

A Right TriangleA Right Triangle

3, 4, 53, 4, 5FamilyFamily6,8,106,8,10

30,40,5030,40,5015,20,2515,20,25

5, 12, 135, 12, 13FamilyFamily

10,24,2610,24,2625,60,6525,60,6535,84,9135,84,91