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

Question

Are there 24 pairs of perpendicular lines in a cube?

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

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:

$4\times6=24$

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

Yes