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Transparency 3. Click the mouse button or press the Space Bar to display the answers. Splash Screen. Example 3-5b. Objective. Find length using the Pythagorean Theorem. Example 3-5b. Vocabulary. Leg. Either of the two sides that form the right angle of a right triangle. legs.

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  1. Transparency 3 Click the mouse button or press the Space Bar to display the answers.

  2. Splash Screen

  3. Example 3-5b Objective Find length using the Pythagorean Theorem

  4. Example 3-5b Vocabulary Leg Either of the two sides that form the right angle of a right triangle legs

  5. Example 3-5b Vocabulary Hypotenuse The side opposite the right angle in a right triangle Hypotenuse

  6. Example 3-5b Vocabulary Pythagorean Theorem In a right triangle, the square of the length of the hypotenuse is equal to the sum of the squares of the lengths of the legs C2 = A2 + B2 Legs Hypotenuse

  7. Example 3-5b Vocabulary Right triangle A triangle with exactly one angle that measures 900

  8. Lesson 3 Contents Example 1Find the Length of the Hypotenuse Example 2Find the Length of a Leg Example 3Solve a Real-Life Problem Example 4Identify Right Triangles Example 5Identify Right Triangles

  9. Example 3-1a GYMNASTICSA gymnastics tumbling floor is in the shape of a square with sides 12 meters long. If a gymnast flips from one corner to the opposite corner, about how far has he flipped? Draw the picture Draw the right angle Remember: The legs come off the right angle The hypotenuse is the diagonal (the longest side)

  10. Example 3-1b To solve, find the length of the hypotenuse c. Write Pythagorean Theorem and bwith 12. Replace a with 12 Evaluate Add. 1/5

  11. Example 3-1b Ask what is being done to the variable The variable is being squared Do the inverse on both sides of the equal sign The inverse of squaring is the square root c c = 16.97 Find the square root of c2 (c  c = c2) Find the square root of 288 Add dimensional analysis c = 16.97 Answer: 1/5

  12. Example 3-1b Add dimensional analysis Answer: meters c = 16.97 1/5

  13. Example 3-1c SEWINGRose has a rectangular piece of fabric measuring 28 inches in length and 16 inches in width. She wants to decorate the fabric with a piece of lace sewn across both diagonals. How much lace will Rose need to complete the project? Draw picture and label dimensions before solving Answer: c = 64.50 inches 1/5

  14. Example 3-2a Find the missing measure of the triangle below. Write the Pythagorean Theorem Replace cwith 15. Replace b with 9 2/5

  15. Example 3-2b Find 152 Find 92 255 = a2 + 81 Ask “what is being done to the variable?” The variable is being added by 81 Do the inverse on both sides of the equal sign 2/5

  16. Example 3-2b Bring down 255 Subtract 81 Bring down = a2 + 81 255 = a2 + 81 255 - 81 = a2 + 81 - 81 144 = a2 + 0 Subtract 81 Combine “like” terms Bring down = a2 Combine “like” terms 2/5

  17. Example 3-2b Use the Identity Property to add a2 + 0 Ask “what is being done to the variable?” 255 = a2 + 81 255 - 81 = a2 + 81 - 81 144 = a2 + 0 The variable is being squared 144 = a2 Do the inverse on both sides of the equal sign Find the square root of both sides of the equal sign 2/5

  18. Example 3-2b Find the square root of 144 Find the square root of a2 255 = a2 + 81 255 - 81 = a2 + 81 - 81 144 = a2 + 0 Add dimensional analysis 144 = a2 Answer: 12 = cm a 2/5

  19. Example 3-2c Find the missing measure of the triangle below. Round to the nearest hundredth if necessary. Draw the picture before solving Answer: a = 18.73 in. 2/5

  20. Example 3-3a TELEVISIONTelevisions are measured according to their diagonal measure. If the diagonal of a television is 36 inches, and its height is 21.6 inches, what is its width? Draw the picture before solving Include the dimensions of each leg and the diagonal 3/5

  21. Example 3-3b Write the Pythagorean Theorem Since c is the diagonal replace c with 36 3/5

  22. Example 3-3b A is the height of the TV so replace a with 21.6 B is the width of the TV so define your variable as b 3/5

  23. Example 3-3b Find 362 Find 21.62 Bring down + b2 1,296 = 466.56 + b2 Ask “what is being done to the variable?” The variable is being added by 466.56 Do the inverse on both sides of the equal sign 3/5

  24. Example 3-3b Bring down 1,296 Subtract 466.56 Bring down = 466.56 1,296 = 466.56 + b2 - 466.56 1,296 = 466.56 - 466.56 + b2 Subtract 466.56 Bring down + b2 3/5

  25. Example 3-3b Combine “like” terms Bring down = Combine “like” terms Use the Identity Property to add 0 + b2 1,296 = 466.56 + b2 - 466.56 1,296 = 466.56 - 466.56 + b2 829.44 = 0 + b2 Ask “what is being done to the variable?” 829.44 = b2 The variable is being squared Find the square root of both sides of the equal sign 3/5

  26. Example 3-3b Find the square root of 829.44 Find the square root of b2 1,296 = 466.56 + b2 - 466.56 1,296 = 466.56 - 466.56 + b2 829.44 = 0 + b2 829.44 = b2 Add dimensional analysi Answer: 28.80 In. = b 3/5

  27. Example 3-3c SWIMMINGThe diagonal of a rectangular swimming pool measures 60 feet. Find the length of the pool if the width measures 30 feet. Round to the nearest hundredth if necessary. Answer: b = 51.96 ft 3/5

  28. Example 3-4a Determine whether a triangle with the lengths 2.5 centimeters, 6 centimeters, and 6.5 centimeters is a right triangle. Write the Pythagorean Theorem 6.52 = 2.52 + 62 Remember c is the longest side so replace c with 6.5 A is the shortest side so replace a with 2.5 B is the remaining leg so replace b with 6 4/5

  29. Example 3-4a Determine whether a triangle with the lengths 2.5 centimeters, 6 centimeters, and 6.5 centimeters is a right triangle. Find 6.52 Find 2.52 6.52 = 2.52 + 62 Find 62 42.25 = 6.25 + 36 Combine “like” terms 42.25 = 42.25 Both sides of the equal sign have the same value Answer: The triangle is a right triangle. If both are equal, then the triangle is a right triangle 4/5

  30. Example 3-4b Determine whether a triangle with the lengths 5 inches, 12 inches, and 13 inches is a right triangle. Answer: the triangle is a right triangle 4/5

  31. Example 3-5a Determine whether a triangle with the lengths 5 feet, 6 feet, and 8 feet is a right triangle. Write the Pythagorean Theorem 82 = 52 + 62 Remember c is the longest side so replace c with 8 A is the shortest side so replace a with 5 B is the remaining leg so replace b with 6 5/5

  32. Example 3-5a Determine whether a triangle with the lengths 5 feet, 6 feet, and 8 feet is a right triangle. Find 82 Find 52 82 = 52 + 62 Find 62 64 = 25 + 36 Combine “like” terms Both sides of the equal sign do not have the same value 64 = 61 Answer: It is not a right triangle Since both sides are not equal, it cannot be a right triangle 5/5

  33. Example 3-5b Determine whether a triangle with the lengths 4.5 centimeters, 9 centimeters, and 12.5 centimeters is a right triangle. Answer: It is not a right triangle 5/5

  34. End of Lesson 3 Assignment

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