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The Pythagorean Theorem

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8/18/20152 The Pythagorean Theorem “For any right triangle, the sum of the areas of the two small squares is equal to the area of the larger.” a 2 + b 2 = c 2 a 2 + b 2 = c 2

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What is the Pythagorean Theorem used for? to find the length of a missing side in a right triangle 5 4 n

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Pythagorean Theorem Formula a 2 + b 2 = c 2 c represents the hypotenuse a and b represent the legs

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hypotenuse leg a b c

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Important bits of information The Pythagorean Theorem can only be used on a right triangle. The legs are always the sides adjacent (next to) the 90 degree angle. It does not matter which leg is a and which leg is b. c is always the hypotenuse (the slant)

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What is the length of the hypotenuse in the triangle below? 2 4 h a 2 + b 2 = c 2

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Plug in the value for each variable in the formula.

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What is the length of the hypotenuse in the triangle below? 2 4 h a 2 + b 2 = c 2 2 2 + 4 2 = h 2 4 + 16 = h 2 20 = h 2

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What is the length of the hypotenuse in the triangle below? 2 4 h a 2 + b 2 = c 2 2 2 + 4 2 = h 2 4 + 16 = h 2 20 = h 2 20= h 4.47 ~ ~ h

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Try this one... Find the hypotenuse of the right triangle below? 6 4 h

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6 4 h a 2 + b 2 = c 2 4 2 + 6 2 = h 2 16 + 36 = h 2 52 = h 2 52 = h 7.21 = h

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What is the length of the missing leg in the triangle below? 3 x 5 a 2 + b 2 = c 2 Try this one...

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Find the hypotenuse of the right triangle below? 5 3 x a 2 + b 2 = c 2 3 2 + x 2 = 5 2 9 + x 2 = 25 x 2 = 16 16 x = 4 -9 - 9

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8/18/201515 Ladder Problem A ladder leans against a second-story window of a house. If the ladder is 25 meters long, and the base of the ladder is 7 meters from the house, how high is the window?

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8/18/201516 Ladder Problem Solution First draw a diagram that shows the sides of the right triangle. Label the sides: –Ladder is 25 m –Distance from house is 7 m Use a 2 + b 2 = c 2 to solve for the missing side. Distance from house: 7 meters

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17 Ladder Problem Solution 7 2 + b 2 = 25 2 49 + b 2 = 625 b 2 = 576 b = 24 m How did you do?

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