1 / 6

Using the Pythagorean Theorem in 3-Dimensional Shapes

Learn to apply Pythagorean Theorem in 3D figures to find diagonals and lengths of segments. Uncover hidden right triangles in prisms and cones for accurate calculations. Understand how to find the diagonal of a 3D prism or the slant height of a cone.

sjulio
Download Presentation

Using the Pythagorean Theorem in 3-Dimensional Shapes

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  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 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? 12 m 5 m

  4. 3D Figures To Find the Diagonal of a 3D Prism To Find the slant height of a cone or pyramid • Diagonals of prisms have a different formula • (length)2+ (width)2 + (height)2 = (diagonal of prism)2 • It doesn’t matter that it is 3D, there is a right triangle hidden in the problem • The slant height is just the hypotenuse of a right triangle. • Use a2 + b2 = c2

  5. 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 differently. • To find AF we need to know the length, width and height of the prism (because it is a 3D shape, we need 3 measurements) • What is the length = AB? • What is the width = FG? • What is the height = GB? • (length)2 + (width)2 + (height)2= (diagonal of prism)2 • 62 + 22+ 32= d2 • 36 + 4 + 9 = d2 • 49 = d2 • 7 = d 6cm 6 cm 2 cm 3 cm The length of the diagonal AF is 7 cm.

  6. Use the Pythagorean Theorem to find the length of diagonal TX. • TX is the diagonal going through a prism. To find TX, we use the Pythagorean Theorem differently. • What is the length = TU? • What is the width = XW? • What is the height = UW? • (length)2 + (width)2 + (height)2= (diagonal of prism)2 • 122 + 62+ 92= d2 • 144 + 36 + 81 = d2 • 261 = d2 • = d 12 in 6 in 9 in The length of the diagonal TX is which is between 16 and 17 inches.

More Related