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Using the Pythagorean Theorem in 3-Dimensional Shapes

Using the Pythagorean Theorem in 3-Dimensional Shapes. Pythagorean Theorem Review. The Pythagorean Theorem states: in any right triangle, the square of the hypotenuse is equal to the sum of the squares of the other two sides. a 2 + b 2 = c 2 Find the length of AC in the diagram below:. c.

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Using the Pythagorean Theorem in 3-Dimensional Shapes

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  1. Using the Pythagorean Theorem in 3-Dimensional Shapes

  2. Pythagorean Theorem Review • The Pythagorean Theorem states:in any right triangle, the square of the hypotenuse is equal to the sum of the squares of the other two sides. a2 + b2 = c2 • Find the length of AC in thediagram below: c a b a2 + 52 = 132 a2 + 25 = 169 a2 = 144 a = 12

  3. 3-Dimensional Figures • How would you find the length of segment AF? • Do you see a right triangle inside the shape? • How would you find the length of segment AV? • Do you see the right triangle inside the shape? 12 m 5 m

  4. Use the Pythagorean Theorem to find the length of diagonal AF. G • To find AF we need the lengths of sides AC and CF. • What is the length of CF? • What is the length ofAC? • Since we do not have the length of AC, but we do have the lengths of AB and CB. We can use the Pythagorean Theorem to find AC. • a2 + b2 = c2 • 62 + 22 = c2 • 36 + 4 = c2 • 40 = c2 • = c 6cm 3 cm We don’t know.

  5. Use the Pythagorean Theorem to find the length of diagonal AF. G • The length of AC = • Now that we have AC and CF, we can usethose numbers to find AF. • a2 + b2 = c2 • ( )2 + 32 = c2 • 40 + 9 = c2 • 49 = c2 • 7 = c • The length of side AF is 7 cm. 6cm

  6. Use the Pythagorean Theorem to find the length of diagonal AV. • To find AVwe need the lengths of sides AMand MV. • What is the length ofMV? • What is the length ofAC? • We have enough information to solve the problem. • a2 + b2 = c2 • 52 + 122 = c2 • 25 + 144 = c2 • 169 = c2 • 13 = c 12 m 12 m 5 m 5 m The length of diagonal AV is 13 m.

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