11.4 Pythagorean Theorem.

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Created by G. Antidormi 2003 The Pythagorean Theorem.

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Presentation transcript:

11.4 Pythagorean Theorem

Pythagorean Theorem hypotenuse c a For a right triangle: a2 + b2 = c2 legs

Find the missing length. a2 + b2 = c2 c 32 + 42 = c2 3 9 + 16 = c2 25 = c2 4 √25 = √c2 5 = c

Find the missing length. a2 + b2 = c2 c 22 + 112 = c2 11 4 + 121 = c2 2 √125 = c2 5√5 = c

Find the value of x. a2 + b2 = c2 (x+2)2 + (x)2 = (√10)2 x + 2 √10 We reject the x=-3, b/c we cannot have negative dimensions 2x(x + 3) -2(x + 3) =0 (2x -2)(x + 3) =0 x = ___ or x =____ -3 1

Find the value of x. x + 3 a2 + b2 = c2 (x+1)2 + (x + 3)2 = (2 √5)2 x2 + 2x + 1+ x2 + 6x + 9 = (2 √5)2 2x2 + 8x + 10 = 20 2x2 + 8x -10 = 0 2x2 + 10x - 2x -10 = 0 2x(x + 5) - 2(x + 5) = 0 -5 X = ____ X = _______ 1 (2x – 2)(x + 5) = 0

Yes it is a right triangle! Determine whether the triangle with the given side lengths is a right triangle. 7, 25, 24 a2 + b2 = c2 72 + 242 = 252 49 + 576 = 625 625 = 625 Yes it is a right triangle!

No, it is not a right triangle! Determine whether the triangle with the given side lengths is a right triangle. 3, 8, 10 a2 + b2 = c2 32 + 82 = 102 9 + 64 = 100 73 = 100 No, it is not a right triangle!

Find the length of the third side. a = 3, c = 7 b = ? a2 + b2 = c2 32 + b2 = 72 9 + b2 = 49 √ √ b2 = 40 b = 2√10