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Converse of the Pythagorean Theorem and Word Problems

pre algebra<br>a^2 b^2 = c^2

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Converse of the Pythagorean Theorem and Word Problems

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  1. Wednesday

  2. Solve for the missing side for each triangle below. Show your work and round your answer to the tenths place. Name- _______________________________ Warm-Up Date-________________________________Quarter 4 Formula: a2 + b2 = c2 Formula: ___________ Formula: ___________

  3. Answer Key

  4. Answer Key

  5. Answer Key

  6. Click here to view video. Start at 11:37

  7. Practice: Converse of Pythagorean Theorem Gallery walk

  8. Gallery Walk : Converse of Pythagorean Theorem Prove whether or not the triangle is a right triangle. 15 cm 10 cm 12 cm #1

  9. Gallery Walk : Converse of Pythagorean Theorem Prove whether or not the triangle is a right triangle. a2 + b2 = c2 102 + 122 = 152 100 + 144 = 225 244 = 225 NOT true NOT a Right Triangle 15 cm 10 cm 12 cm #1

  10. Gallery Walk : Converse of Pythagorean Theorem Prove whether or not the triangle is a right triangle. 5 cm 3 cm 4 cm #2

  11. Gallery Walk : Converse of Pythagorean Theorem Prove whether or not the triangle is a right triangle. a2 + b2 = c2 32 + 42 = 52 9 + 16 = 25 25 = 25 True Is a Right Triangle 15 cm 10 cm 12 cm #2

  12. Gallery Walk : Converse of Pythagorean Theorem Prove whether or not the triangle is a right triangle. 18 cm 19 cm 22 cm #3

  13. Gallery Walk : Converse of Pythagorean Theorem Prove whether or not the triangle is a right triangle. 18 cm a2 + b2 = c2 182 + 192 = 222 324 + 361 = 484 685 = 484 NOT true NOT a Right Triangle 19 cm 22 cm #3

  14. Gallery Walk : Converse of Pythagorean Theorem Prove whether or not the triangle is a right triangle. 19 cm 17 cm 30 cm #4

  15. Gallery Walk : Converse of Pythagorean Theorem Prove whether or not the triangle is a right triangle. a2 + b2 = c2 192 + 172 = 302 361 + 289 = 900 650 = 900 NOT a true NOT a Right Triangle 19 cm 17 cm 30 cm #4

  16. Gallery Walk : Converse of Pythagorean Theorem Prove whether or not the triangle is a right triangle. 8 cm 7 cm 6 cm #5

  17. Gallery Walk : Converse of Pythagorean Theorem Prove whether or not the triangle is a right triangle. a2 + b2 = c2 72 +62 = 82 49 + 36 = 64 85 = 64 NOT a true NOT a Right Triangle 8 cm 7 cm 6 cm #5

  18. Gallery Walk : Converse of Pythagorean Theorem Prove whether or not the triangle is a right triangle. 145 cm 17 cm 144 cm #6

  19. Gallery Walk : Converse of Pythagorean Theorem Prove whether or not the triangle is a right triangle. a2 + b2 = c2 172 + 1442 = 1452 289 + 20736 = 21025 21025 = 21025 True Is a Right Triangle 145 cm 17 cm 144 cm #6

  20. Gallery Walk : Converse of Pythagorean Theorem Prove whether or not the triangle is a right triangle. 101 cm 20 cm 99 cm #7

  21. Gallery Walk : Converse of Pythagorean Theorem Prove whether or not the triangle is a right triangle. a2 + b2 = c2 202 + 992 = 1012 400 + 9801 = 10201 10201 = 10201 True Is a Right Triangle 101 cm 20 cm 99 cm #7

  22. Gallery Walk : Converse of Pythagorean Theorem Prove whether or not the triangle is a right triangle. 11 cm 5 cm 13 cm #8

  23. Gallery Walk : Converse of Pythagorean Theorem Prove whether or not the triangle is a right triangle. 11 cm a2 + b2 = c2 112 + 52 = 132 121 + 25 = 169 145 = 169 NOT a true NOT a Right Triangle 5 cm 13 cm #8

  24. Steps to follow with word problems: Step 1: Draw a picture. Step 2: Fill in the given information on the picture. Step 3: Identify the legs and hypotenuse. Step 4: Substitute the legs and hypotenuse into the formula. Step 5: Solve

  25. Let’s try one together. A baseball diamond is a square that is 90 ft on each side. What is the distance a catcher has to throw the ball from home to second base?

  26. Let’s try one together. Step 1: Draw a picture. A baseball diamond is a square that is 90 ft on each side. What is the distance a catcher has to throw the ball from home to second base? 2nd X base Home X plate

  27. Let’s try one together. A baseball diamond is a square that is 90 ft on each side. What is the distance a catcher has to throw the ball from home to second base? Step 1: Draw a picture. 2nd X base 90 ft. Step 2: Fill in the given information on the picture. 90 ft. Home X plate

  28. Let’s try one together. A baseball diamond is a square that is 90 ft on each side. What is the distance a catcher has to throw the ball from home to second base? Step 1: Draw a picture. LEGS 2nd X base 90 ft. Step 2: Fill in the given information on the picture. Hypotenuse Step 3: Identify the Legs and Hypotenuse. 90 ft. LEGS Home X plate

  29. Let’s try one together. Formula: a2 + b2 = c2 902 + 902 = c2 A baseball diamond is a square that is 90 ft on each side. What is the distance a catcher has to throw the ball from home to second base? Step 4: Substitute the legs and hypotenuse into the formula.

  30. Let’s try one together. Formula: a2 + b2 = c2 902 + 902 = c2 8100 + 8100 = c2 16200 = c2 16200 = c2 127.3 ft (rounded to nearest tenth) A baseball diamond is a square that is 90 ft on each side. What is the distance a catcher has to throw the ball from home to second base? Step 5: Solve

  31. Let’s try another one.

  32. A 35-foot ladder is leaning against the side of a building and is positioned such that the base of the ladder is 21 feet from the base of the building. How far above the ground is the point where the ladder touches the building?

  33. A 35-foot ladder is leaning against the side of a building and is positioned such that the base of the ladder is 21 feet from the base of the building. How far above the ground is the point where the ladder touches the building?

  34. Formula: a2 + b2 = c2 212 + b2 = 352 441 + b2 = 1225 -441 = -441 b2 = 784 b = 784 b = 28 ft A 35-foot ladder is leaning against the side of a building and is positioned such that the base of the ladder is 21 feet from the base of the building. How far above the ground is the point where the ladder touches the building? b = 28 ft The ladder touches the building 28 feet above the ground.

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