Look at the dotted diagonal in the figure below.
Which diagonals of the rectangular prism are equal?
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Look at the dotted diagonal in the figure below.
Which diagonals of the rectangular prism are equal?
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:
Below is a cuboid with a length of
8 cm.
Its width is 2 cm and its height is
4 cm.
Calculate the volume of the cube.
All space diagonals are equal because they span the same three dimensions. Each diagonal like AH, BG, and FC connects vertices that are separated by the full length, width, and height of the prism.
A space diagonal must connect two vertices that are opposite corners of the rectangular prism. Look for lines that go through the interior, not along faces or edges.
ED is a face diagonal that lies flat within one rectangular face. It's shorter than space diagonals because it only spans two dimensions (length and width) instead of all three.
Yes! A rectangular prism has 4 space diagonals total. Besides AH, BG, and FC, there's also diagonal EG. All four space diagonals have equal length.
Opposite vertices are separated by the maximum distance possible in the prism. If you can travel along three perpendicular edges to get from one vertex to another, they're opposite.
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