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Pythagorean Theorem In a right triangle with sides of length a and b and hypotenuse c : a 2 + b 2 = c 2 MA202 Sections 5 & 401 Chapter 12-3 Slides Proving the Pythagorean Theorem MA202 Sections 5 & 401 Chapter 12-3 Slides Proving the

  1. Pythagorean Theorem In a right triangle with sides of length a and b and hypotenuse c : a 2 + b 2 = c 2 MA202 Sections 5 & 401 Chapter 12-3 Slides

  2. Proving the Pythagorean Theorem MA202 Sections 5 & 401 Chapter 12-3 Slides

  3. Proving the Pythagorean Theorem MA202 Sections 5 & 401 Chapter 12-3 Slides

  4. Example 12.16 MA202 Sections 5 & 401 Chapter 12-3 Slides

  5. Converse of the Pythagorean Theorem If you have a triangle with sides of length a , b , and c , where a 2 + b 2 = c 2 : then the triangle is a right triangle with hypotenuse the side of length c . MA202 Sections 5 & 401 Chapter 12-3 Slides

  6. Example 12.18 Determine if each of the following is a right triangle: 15 , 17 , 8 MA202 Sections 5 & 401 Chapter 12-3 Slides

  7. Example 12.18 Determine if each of the following is a right triangle: ( Yes, 8 2 + 15 2 = 64 + 225 = 289 = 17 2 ) 15 , 17 , 8 MA202 Sections 5 & 401 Chapter 12-3 Slides

  8. Example 12.18 Determine if each of the following is a right triangle: ( Yes, 8 2 + 15 2 = 64 + 225 = 289 = 17 2 ) 15 , 17 , 8 √ 10 , 5 , 5 3 MA202 Sections 5 & 401 Chapter 12-3 Slides

  9. Example 12.18 Determine if each of the following is a right triangle: ( Yes, 8 2 + 15 2 = 64 + 225 = 289 = 17 2 ) 15 , 17 , 8 √ √ ( Yes, 5 2 + (5 3) 2 = 25 + 75 = 100 = 10 2 ) 10 , 5 , 5 3 MA202 Sections 5 & 401 Chapter 12-3 Slides

  10. Example 12.18 Determine if each of the following is a right triangle: ( Yes, 8 2 + 15 2 = 64 + 225 = 289 = 17 2 ) 15 , 17 , 8 √ √ ( Yes, 5 2 + (5 3) 2 = 25 + 75 = 100 = 10 2 ) 10 , 5 , 5 3 5 , 11 , 12 MA202 Sections 5 & 401 Chapter 12-3 Slides

  11. Example 12.18 Determine if each of the following is a right triangle: ( Yes, 8 2 + 15 2 = 64 + 225 = 289 = 17 2 ) 15 , 17 , 8 √ √ ( Yes, 5 2 + (5 3) 2 = 25 + 75 = 100 = 10 2 ) 10 , 5 , 5 3 ( No, 5 2 + 11 2 = 25 + 121 = 146 � = 12 2 ) 5 , 11 , 12 MA202 Sections 5 & 401 Chapter 12-3 Slides

  12. Class Discussion In a square based right regular pyramid, the height off the square is measured from the center of the square. For some of the homework, remember the formulas for area from the previous section. MA202 Sections 5 & 401 Chapter 12-3 Slides

  13. Class Discussion Solve for x in the following figure: MA202 Sections 5 & 401 Chapter 12-3 Slides

  14. Class Discussion Solve for y in the following figure: MA202 Sections 5 & 401 Chapter 12-3 Slides

  15. Class Discussion Solve for x and y in the following figure: MA202 Sections 5 & 401 Chapter 12-3 Slides

  16. Class Discussion Find the area of the equilateral triangle: MA202 Sections 5 & 401 Chapter 12-3 Slides

  17. Homework Homework 7 (due 4/6/10): Section 12.3 # 2ac, 3, 4ab, 5, 6, 9, 32 Section 12.4 # 2b, 3c, 4d, 5d, 6ab, 19a, 23 MA202 Sections 5 & 401 Chapter 12-3 Slides

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