Just as a line is made of an infinite number of points, a plane is made of an infinite number of lines that are right next to each other.
A plane is flat, and it goes on infinitely in all directions. A sheet of paper represents a small part of one plane. But actually a sheet of paper is much thicker than a plane, because a plane has no thickness. It is only as thick as a point, which takes up no space at all. So a plane is like an imaginary sheet of paper, infinitely wide and long, but with no thickness.
When we talk about a triangle or a square, these shapes are like pieces cut out of a plane, as if you had cut them out of a piece of paper. But is there another way to create these polygons or other shapes like circles?
Some geometers are very interested what happens when a plane intersects or cuts a 3-Dimensional shape.
Examine the GeoGebra workspace.
The blue rectangle represents, like a piece of paper, a small part of a plane cutting through a cone.
The red shape represents the shape that would be formed if the plane actually cut the cone.
The green points are drag points that can be used to reorient the intersecting plane.
Use the various sliders to experiment with different “slices” of the cube.
Observe what shapes are created when a plane slices through a cone.
What shapes did you observe?