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The Pythagorean Theorem

The Pythagorean Theorem. The Pythagorean Theorem. Given any right triangle, A 2 + B 2 = C 2. C. A. B. Example. 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. C. A. B.

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The Pythagorean Theorem

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  1. The Pythagorean Theorem

  2. The Pythagorean Theorem Given any right triangle, A2 + B2 = C2 C A B

  3. Example In the following figure if A = 3 and B = 4, Find C. A2 + B2 = C2 32 + 42 = C 2 9 + 16 = C2 5 = C C A B

  4. 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 A = 6, B = 8, Find C 6) A = 9, B = 12, Find C Practice C = 17 C = 25 C A C = 41 C = 26 B C = 10 C = 15

  5. Example In the following figure if B = 5 and C = 13, Find A. A2 + B2 = C2 A2 +52 = 132 A2 + 25 = 169 A2 = 144 A = 12 C A B

  6. A=8, C =10 , Find B A=15, C=17 , Find B B =10, C=26 , Find A A =12, C=16, Find B 5) B =5, C=10, Find A A=11, C=21, Find B Practice B = 6 B = 8 A = 24 C A B = 10.6 A = 8.7 B B = 17.9

  7. “Real-World” The top of a ladder rests against a wall, 23 feet above the ground. The base of the ladder is 6 feet away from the wall. What is the length of the ladder? Step 1: Draw a sketch and label the parts. Step 2: Determine whether you are looking for the leg or hypotenuse of the right triangle. Step 3: Solve the missing length.

  8. AREA Find the area of each figure 1. 2.

  9. Given the lengths of three sides, how do you know if you have a right triangle? Given A = 6, B=8, and C=10, describe the triangle. A2 + B2 = C2 62 +82 = 102 36 + 64 = 100 100 = 100 This is true, so you have a right triangle. C A B

  10. Given A = 4, B = 5, and C =6, describe the triangle. C2 = A2 + B2 62 = 42 + 52 36 = 16 + 25 36 < 41 36 < 41, so we have an acute triangle. If C2 < A2 + B2 , then you have an acute triangle. A B C

  11. Given A = 4, B = 6, and C =8, describe the triangle. C2 = A2 + B2 82 = 42 + 62 64 = 16 + 36 64 > 52 64 > 52, so we have an obtuse triangle. If C2 > A2 + B2 , then you have an obtuse triangle. A B C

  12. A=10, B=15, C=20 2) A=2, B=5, C=6 3) A=12, B=16, C=20 4) A=11, B=12, C=14 5) A=2, B=3, C=4 6) A=1, B=7, C=7 Describe the following triangles as acute, right, or obtuse obtuse obtuse C right A acute obtuse B acute

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