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1 9.1 and 9.2 The Pythagorean Theorem

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2 A B C Given any right triangle, A 2 + B 2 = C 2

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3 Example A B C In the following figure if A = 3 and B = 4, Find C. A 2 + B 2 = C 2 3 2 + 4 2 = C 2 9 + 16 = C 2 5 = C

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4 You can verify the Pythagorean Theorem with the following: Given a piece of graph paper, make a right triangle. Then make squares of the right triangle. Then find the square’s areas.

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5 Pythagorean Theorem : Examples 1.A=8, B= 15, Find C 2.A=7, B= 24, Find C 3.A=9, B= 40, Find C 4.A=10, B=24, Find C 5. A =6, B=8, Find C A B C C = 17 C = 25 C = 41 C = 26 C = 10

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6 Finding the legs of a right triangle: A B C In the following figure if B = 5 and C = 13, Find A. A 2 + B 2 = C 2 A 2 +5 2 = 13 2 A 2 + 25 = 169 A 2 +25-25=169-25 A 2 = 144 A = 12

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7 More Examples: 1) A=8, C =10, Find B 2) A=15, C=17, Find B 3) B =10, C=26, Find A 4) A=15, B=20, Find C 5) A =12, C=16, Find B 6) B =5, C=10, Find A 7) A =6, B =8, Find C 8) A=11, C=21, Find B A B C B = 6 B = 8 A = 24 C = 25 B = 10.6 A = 8.7 C = 10 B = 17.9

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8 Given the lengths of three sides, how do you know if you have a right triangle? A B C Given A = 6, B=8, and C=10, describe the triangle. A 2 + B 2 = C 2 6 2 +8 2 = 10 2 36 + 64 = 100 This is true, so you have a right triangle.

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9 If A 2 + B 2 > C 2, you have an acute triangle. Given A = 4, B = 5, and C =6, describe the triangle. A 2 + B 2 = C 2 4 2 + 5 2 = 6 2 16 + 25 = 36 41 > 36, so we have an acute triangle. A B C

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10 If A 2 + B 2 < C 2, you have an obtuse triangle. Given A = 4, B = 6, and C =8, describe the triangle. A 2 + B 2 = C 2 4 2 + 6 2 = 8 2 16 + 36 = 64 52 < 64, so we have an obtuse triangle. A C B

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11 Describe the following triangles as acute, right, or obtuse 1) A=9, B=40, C=41 2) A=10, B=15, C=20 3) A=2, B=5, C=6 4) A=12, B=16, C=20 5) A=11, B=12, C=14 6) A=2, B=3, C=4 7) A=1, B=7, C=7 8) A=90, B=120, C=150 A B C right acute obtuse right obtuse acute

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