GeoGebra Classroom

# Crossing Planes

## Instructions

The red plane (f) is an infinite 2D horizontal surface. Turn on the green plane (k) by clicking the circle next to its name in the left panel. Observe how the planes pass through each other, but still continue infinitely and are not split into two different planes. Turn on Points A and B and line g in the left panel. Notice that line g is the intersection of the two planes and Points A and B are shared between the two planes. Turn on Points C, D, and E in the left panel. If you turn off the red plane (f) in the left panel, which points lie on the green plane? If you turn the red plane back on and turn off the green plane (k) in the left panel, which points lie on the red plane? Click and drag to rotate the view and use the mouse wheel to zoom in and out as you work with this construction to view it from other perspectives.

## Reflection

If you rotate the view to look directly down line g, what do you notice? When two planes intersect, what shape do you get as a result? Does it matter that there is a second plane passing between Points C and E? Were they still coplanar when you looked at just the green plane?