Fundamental Concepts
5. The Plane · Length and width — infinite, with no thickness
A plane has length and width but no thickness, and extends infinitely in every direction along its surface.
A plane is a perfectly flat surface with two dimensions — length and width — but no thickness. The yellow line l lies inside the plane: any point on l is on the plane. Move P along the line and you stay on the plane; move P vertically and you drift off the plane (because the plane has no thickness to hold you above or below it).
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For subscribers · Selina ICSE: Fundamental Concepts
What this lesson covers
Try to break it
What happens if we try to lift the line off the surface? A true plane has no edges and no thickness, so the line must stay flat and connected to it.
How you build it
Mark a point on the plane.
- Click the Point tool and drop point P anywhere. Because the plane extends forever, P is always on the plane — no matter where you click.
The proof, step by step
Prove that the surface is a plane — flat and extending without end.
- A plane is a flat surface with length and width but no thickness.
- It extends indefinitely in all directions, having no boundaries.
- If two points lie on a plane, the line containing them also lies on the plane.
Worked example
Which of the following best describes a plane in geometry?
A plane is defined as a flat surface that has length and width but no thickness. It extends indefinitely in all directions and has no boundaries.
- A flat surface with length, width, and thickness
- A flat surface with length and width but no thickness, extending indefinitely — correct
- A curved surface that has boundaries
- A three-dimensional solid object