Sketching planes

Question

1.) Sketch a plane and two intersecting lines that intersect the plane at separate points

 

2.) Sketch a plane and two intersecting lines that do not intersect the plane

 

3.) Sketch a plane and two intersecting line that lie on the plane 

Answer 1

 

1) get a sheet of paper and two pencils.

    With one of the pencils punch a hole in the paper and push the pencil through the paper halfway.

     Do the same thing with the second pencil.

     There's a hands on, live, real, kinesthethic example for problem #1

      The pencils are the lines, the paper is the plane. two of them interest

      at a single point. As long as the lines (pencils) are not parallel, they will intersect.

      

 

2)  The lines are outside the plane.  Get some skotch tape.

      Tape the pencils together so that they form an X.

      Get another piece of tape. Connect one end of the

      tape to the pencils, the other to the paper. Voila! there's problem #2.

 

 3) I think this one is very easy to visualize.