Are there 24 pairs of perpendicular lines in a cube?
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Are there 24 pairs of perpendicular lines in a cube?
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:
Therefore, the number of perpendicular lines in a cube is 24.
Yes
What do the four figures below have in common?
Two lines are perpendicular when they intersect at exactly 90 degrees. In a cube, every corner where two edges meet forms this perfect right angle!
Each face of the cube has 4 corner angles that are 90 degrees. Since a cube has 6 faces, we get: total perpendicular line pairs.
No! Each 90-degree angle represents a unique pair of perpendicular lines. The faces don't share the same corner angles, so each count is distinct.
Look at any corner of a box or room! You'll see three edges meeting at right angles. Each cube face contributes 4 such corners, giving us our 24 total perpendicular pairs.
Only for shapes with right angles! A sphere has no perpendicular lines, while a rectangular prism would also have 24 (if all angles are 90°).
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