Using the Pythagorean Theorem in 3 Dimensional Shapes

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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

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 c + b 2 = c 2 a b �Find the length of AC in the diagram below: a 2 + 52 = 132 a 2 + 25 = 169 a 2 = 144 a = 12

3 -Dimensional Figures 12 m 5 m �How would you find the length of

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

3 D Figures To Find the slant height of a cone or pyramid �

3 D Figures To Find the slant height of a cone or pyramid � It doesn’t matter that it is 3 D, there is a right triangle hidden in the problem � The slant height is just the hypotenuse of a right triangle. � Use a 2 + b 2 = c 2 To Find the Diagonal of a 3 D Prism � Diagonals of prisms have a different formula � (length)2 + (width)2 + (height)2 = (diagonal of prism)2

Use the Pythagorean Theorem to find the length of diagonal AF. G � AF

Use the Pythagorean Theorem to find the length of diagonal AF. G � AF is the diagonal going through a prism. To find AF, we use the Pythagorean Theorem 6 c differently. m � To find AF we need to know the length, width and height of the prism (because it is a 3 D shape, we need 3 measurements) 6 cm � What is the length = AB? 2 cm � What is the width = FG? 3 cm � What is the height = GB? � (length)2 + (width)2 + (height)2 = (diagonal of prism)2 � 62 + 22 + 32 = d 2 � 36 + 4 + 9 = d 2 The length of the diagonal AF is 7 cm. � 49 = d 2 � 7 = d

Use the Pythagorean Theorem to find the length of diagonal TX. � 12 in

Use the Pythagorean Theorem to find the length of diagonal TX. � 12 in 6 in 9 in