Counting Perpendicular Lines in a Cube: Verifying the 24 Pairs Property

Are there 24 pairs of perpendicular lines in a cube?

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Step-by-step video solution

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00:00 Are there 24 perpendiculars in a cube?
00:03 A perpendicular creates a right angle at the intersection point between lines
00:07 Let's mark and count all right angles to find the perpendiculars
00:09 We have 4 perpendiculars in each face
00:15 Let's count the number of faces we have and multiply by the number of perpendiculars
00:22 The fourth face at the bottom is not visible in the drawing
00:28 The back face is also not visible
00:31 As well as the left face
00:34 Let's multiply the number of faces we have (6) by the number of perpendiculars (4)
00:38 And that's the solution to the question

Step-by-step written solution

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1

Understand the problem

Are there 24 pairs of perpendicular lines in a cube?

2

Step-by-step solution

Remember that perpendicular lines form a 90-degree angles.

As we know, in the cube all angles are 90 degrees (right angles).

We will mark the angles of the highlighted face in the following way:

As a cube has 6 faces, we will multiply the number of angles we marked by 6 to get:

4×6=24 4\times6=24

Therefore, the number of perpendicular lines in a cube is 24.

3

Final Answer

Yes

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What do the four figures below have in common?

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