1 / 13

Space Diagonal

Space Diagonal. The Pythagorean Theorem in 3D. In a rectangular prism, a space diagona l is a line that goes from a vertex of the prism , through the center of the prism to the opposite vertex. aka, ‘stick in the box’. A rectangular prism has 4 space diagonals. Space Diagonal.

karik
Download Presentation

Space Diagonal

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. Space Diagonal The Pythagorean Theorem in 3D

  2. In a rectangular prism, a space diagonal is a line that goes from a vertex of the prism, through the center of the prism to the opposite vertex. aka, ‘stick in the box’ A rectangular prism has 4 space diagonals.

  3. Space Diagonal The Pythagorean Theorem is useful when we need to find the length of a space diagonal in a rectangular prism. Side c is the space diagonal.

  4. Finding The Length Of A Space Diagonal. H G E F 16cm D C 12cm C 28cm A B 12 A 28 Look at the rectangular prism below: It is our task to calculate the length of the space diagonal AG which runs through the space inside the rectangular prism. • Start by considering the triangle ABC. (2) Calculate the length of AC. AC ≈ 30.5cm B

  5. H G E 16cm F G D 16 C A 12cm 30.5cm 30.5 28cm A B Now look at the box again. (3) Now consider triangle ACG. (4) Calculate the length of AG. C AG = AG = 34.4cm

  6. OR OR OR OR OR OR OR OR OR

  7. A diagonal of a three-dimensional figure connects two vertices of two different faces. Diagonal d of a rectangular prism is shown in the diagram. By the Pythagorean Theorem, l2 + w2 = x2 and x2 + h2 = d2. Using substitution,d2 =l2 + w2 + h2.

  8. d c b Pythagorean Theorem2D vs 3D

  9. The Space Diagonal d2 = l2 + w2 + h2.

  10. H G E F 16cm D C 12cm A 28cm B Space DiagonalPythagoras In 3D Shapes.

  11. (1) (2) 23cm 12m 17cm 3m 26cm 4m What Goes In The Box ? Calculate the lengths of the space diagonals in the rectangular prisms below:

  12. Using the Pythagorean Theorem in Three Dimensions Find the length of the space diagonal of a 6 cm by 8 cm by 10 cm rectangular prism Substitute Simplify

  13. Using the Pythagorean Theorem in Three Dimensions Find the height of a rectangular prism with a 12 in. by 7 in. base and a space diagonal of 15 in. Substitute Square both sides of the equation. Simplify. 225 = 144 + 49 + h2 Solve for h2. h2 = 32 Take the square root of both sides.

More Related