GeoGebra 3D: Getting Started - Part 2


Construct a plane that passes through 3 non-collinear points. Be sure this plane is not parallel to the gray plane. Also be sure this plane does not coincide (i.e. "lie on" or is identical to) the gray plane itself.


How would you describe the intersection of the gray plane and the plane you've just constructed? Use another GeoGebra tool to verify your assertion is true. In general, what can we conclude about the intersection of any 2 non-parallel planes?

In the GeoGebra applet below, 1) Construct a sphere. 2) Construct a plane that slices through this sphere (other than the given gray plane.) 3) Now hide the given gray plane by right clicking on it and unchecking "Show Plane". 4) Plot the intersection of this plane and sphere. 5) Select the blue MOVE arrow. Now move the plane around. As you do, carefully observe the intersection of the plane and this sphere. Please answer the question below.

How would you describe the intersection of this plane and sphere? How can we use GeoGebra to informally conclude your assertion is correct? Please describe below and then do so.