GeoGebra Classroom

# Plane Crossing Plane: What Do We Get?

## DIRECTIONS:

1) Select the POINT tool. Use this tool to plot 3 points anywhere on the gray plane. 2) Select the MOVE arrow. Click twice on any one of the points you plotted in step (1). Use this tool to move this point off of the gray plane. Repeat this process for the other 2 points. 3) Select the PLANE THROUGH 3 POINTS tool. With this tool highlighted, select the 3 points you initially plotted in step (1). This will create a plane that passes through these 3 points. Further directions appear below this applet.
4) Select the MOVE arrow. Use this tool to drag any one (or more) of these 3 points around. Notice how the plane you plotted in (3) always passes through these 3 points. 5) Now select the INTERSECT 2 SURFACES tool. Select the plane you plotted in step (3). Then select the gray plane. This will now plot the intersection of these 2 surfaces (here, planes). 6) Select the MOVE tool again. Drag any 1 (or more) of the 3 points you plotted in the first step. Then answer the question that follows.

## QUESTION:

What can we conclude about the intersection of any 2 non-parallel planes?