Rectangular Prism Diagonals: Identifying Equal Interior Lines in 3D Geometry

Look at the dotted diagonal in the figure below.

Which diagonals of the rectangular prism are equal?

AAABBBCCCDDDEEEFFFGGGHHH

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations
00:06 How many matching diagonals are there with the one we've drawn? Let's find out!
00:11 Imagine the face of a box. Each face is a rectangle.
00:16 In a rectangle, both diagonals are exactly the same length.
00:21 A box has opposite faces that are identical.
00:31 So, equal rectangles mean all their diagonals are equal too!
00:42 And that's how we solve this question!

Step-by-step written solution

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1

Understand the problem

Look at the dotted diagonal in the figure below.

Which diagonals of the rectangular prism are equal?

AAABBBCCCDDDEEEFFFGGGHHH

2

Step-by-step solution

Let's look at the face AEHD

In it, there is another diagonal equal to ED, which is AH

Let's look at the face BFGC which is identical and equal to AEHD, in which there are two diagonals that are also equal to ED:

FC=BG=ED FC=BG=ED

3

Final Answer

AH,BG,FC AH,BG,FC

Practice Quiz

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A cuboid is shown below:

222333555

What is the surface area of the cuboid?

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