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Pythagorean Theorem 3D

8th grade math<br>pre algebra<br>geometry<br>3-D

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Pythagorean Theorem 3D

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  1. April 28th • Thursday To Do List: Agenda: Outcome: Take out your hot pink Warm-Up paper. Get a calculator. Check over the Warm-Up Practice Problems- Pythagorean Theorem with 3-D diagonals. Students will apply the Pythagorean Theorem with 3-D diagonals. DELTAMATH-HW #2: Due by Friday, 4/29

  2. PURPLE WARM UP: The area of a rectangle is 105 square units. Its width measures 7 units. Find the length of its diagonal. Fill in the information Hint: This problem requires 2 steps.

  3. PURPLE WARM UP: The area of a rectangle is 105 square units. Its width measures 7 units. Find the length of its diagonal. Hint: This problem requires 2 steps.

  4. PURPLE WARM UP: The area of a rectangle is 105 square units. Its width measures 7 units. Find the length of its diagonal. Hint: This problem requires 2 steps. diagonal:

  5. Answer Key

  6. Graph a right triangle with the two points forming the hypotenuse. Using the sides, find the distance between the two points in simplest radical form. • Orange Warm-Up Leg- ___________ Leg- ___________ Hypotenuse- __________ ?

  7. Graph a right triangle with the two points forming the hypotenuse. Using the sides, find the distance between the two points in simplest radical form. • Answer Key Leg- 8 units Leg- 6 units Hypotenuse- 10 units ?

  8. Graph a right triangle with the two points forming the hypotenuse. Using the sides, find the distance between the two points. (-7,5) and (-2, -7) BLUE WARM-UP Find the hypotenuse. Now find the perimeter. Leg- Leg- Hypotenuse- Perimeter: ?

  9. Graph a right triangle with the two points forming the hypotenuse. Using the sides, find the distance between the two points. (-7,5) and (-2, -7) • Answer Key Now find the perimeter. Leg- 5 units Leg- 12 units Hypotenuse- 13 units Perimeter: 5 + 12 + 13 = 30 units ? 12 units 5 units

  10. Graph the points in order and connect them to reveal a picture. Show your teacher when you are finished. • Green Warm-Up

  11. Answer Key

  12. 3-Dimensional Diagonal _ + _ +_ = _ Height width length

  13. 3-Dimensional Diagonal __ + __ +__ = __ l2 w2 h2 d2 height width length

  14. 3-Dimensional Diagonal __ + __ +__ = __ Or a2 + b2 + c2 = d2 w2 l2 h2 d2 Height width length

  15. The base of the rectangular prism is a _______. Height width length

  16. The base of the rectangular prism is a rectangle. Height width length

  17. The base of the rectangular prism is a rectangle. Height Step 1: c a width b length

  18. The base of the rectangular prism is a rectangle. Height Step 1: a2 + b2 = c2 c a width b length

  19. Find the base of the rectangular prism is a rectangle. Height Step 1: a2 + b2 = c2 c a width b length Step 2: d h c

  20. Find the base of the rectangular prism is a rectangle. Height Step 1: a2 + b2 = c2 c a width b length Step 2: c2 + h2 = d2 d h c

  21. Find the base of the rectangular prism is a rectangle. Height Step 1: a2 + b2 = c2 c a width b length Step 2: c2 + h2 = d2 d h RULE to follow: a2 + b2+ c2= d2 c

  22. Practice: Place the rectangular prisms in order by length of their diagonals. 8cm 5 cm 10 cm B A 10 cm 15 cm C 10 cm 12 cm 10 cm 8 cm

  23. Practice: Place the rectangular prisms in order by length of their diagonals. a2 + b2+ c2= d2 10 cm A 10 cm 10 cm

  24. Practice: Place the rectangular prisms in order by length of their diagonals. a2 + b2+ c2= d2 102 + 102 + 102 = d2 10 cm A 10 cm 10 cm

  25. Practice: Place the rectangular prisms in order by length of their diagonals. a2 + b2+ c2= d2 102 + 102 + 102 = d2 100 + 100 + 100 = d2 10 cm A 10 cm 10 cm

  26. Practice: Place the rectangular prisms in order by length of their diagonals. a2 + b2+ c2= d2 102 + 102 + 102 = d2 100 + 100 + 100 = d2 300 = d2 10 cm A 10 cm 10 cm

  27. Practice: Place the rectangular prisms in order by length of their diagonals. a2 + b2+ c2= d2 102 + 102 + 102 = d2 100 + 100 + 100 = d2 300 = d2 17.32= d 10 cm A 10 cm 10 cm

  28. Practice: Place the rectangular prisms in order by length of their diagonals. a2 + b2+ c2= d2 5 cm B 10 cm 15 cm

  29. Practice: Place the rectangular prisms in order by length of their diagonals. a2 + b2+ c2= d2 102 + 152 + 52 = d2 5 cm B 10 cm 15 cm

  30. Practice: Place the rectangular prisms in order by length of their diagonals. a2 + b2+ c2= d2 102 + 152 + 52 = d2 100 + 225 + 25 = d2 5 cm B 10 cm 15 cm

  31. Practice: Place the rectangular prisms in order by length of their diagonals. a2 + b2+ c2= d2 102 + 152 + 52 = d2 100 + 225 + 25 = d2 350 = d2 5 cm B 10 cm 15 cm

  32. Practice: Place the rectangular prisms in order by length of their diagonals. a2 + b2+ c2= d2 102 + 152 + 52 = d2 100 + 225 + 25 = d2 350 = d2 18.71= d 5 cm B 10 cm 15 cm

  33. Practice: Place the rectangular prisms in order by length of their diagonals. a2 + b2+ c2= d2 8cm C 12 cm 8 cm

  34. Practice: Place the rectangular prisms in order by length of their diagonals. a2 + b2+ c2= d2 82 + 122 + 82 = d2 8cm C 12 cm 8 cm

  35. Practice: Place the rectangular prisms in order by length of their diagonals. a2 + b2+ c2= d2 82 + 122 + 82 = d2 64 + 144 + 64 = d2 8cm C 12 cm 8 cm

  36. Practice: Place the rectangular prisms in order by length of their diagonals. a2 + b2+ c2= d2 82 + 122 + 82 = d2 64 + 144 + 64 = d2 272 = d2 8cm C 12 cm 8 cm

  37. Practice: Place the rectangular prisms in order by length of their diagonals. a2 + b2+ c2= d2 82 + 122 + 82 = d2 64 + 144 + 64 = d2 272 = d2 16.49= d 8cm C 12 cm 8 cm

  38. Practice: Place the rectangular prisms in order by length of their diagonals. 8cm 5 cm 10 cm B A 10 cm 15 cm C 10 cm 12 cm 10 cm 8 cm C , A , B is least to greatest

  39. Which spider thread is closest to the example?

  40. Example 1: 12.5 in. 24 in. 7 in.

  41. Example 1: a2 + b2+ c2= d2 72 + 242 + 12.52 = d2 49 + 576+ 156.25 = d2 781.25 = d2 27.95= d 12.5 in. 24 in. 7 in.

  42. What box is closest the length to the example? : D A B C

  43. What box is closest the length to the example? : D A B C

  44. Example 2: 120 in. 40 in. 30 in.

  45. What box is closest the length to the example? : D A B C

  46. What box is closest the length to the example? : D A B C

  47. Find the measurement of the diagonal of the fish tank. 6 in. 24 in. 18 in.

  48. Pythagorean Theorem in Three Dimensions: a2+b2+c2=d2 62+242+182=d2 36+576+324=d2 936=d2 30.59 = d 30.6in The measurement of diagonal of the Fish tank is 30.6in. 6 in. 24 in. 18 in.

  49. Practice - Pythagorean Theorem

  50. Answers - Pythagorean Theorem

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