Plane ABC and plane BCE ____ be the same plane

Question

select one

a. cannot

b. may

c. must

Answer 1

This is a very important rule:  Three points determine a plane.

 

[ Here is another very important rule:  Two points determine a line. ]

 

So, Plane ABC and plane BCE _may_ be the same plane.  This happens when E is on Plane ABC (or you could say, A is on Plane BCE).  If not, then they are two different planes.

Answer 2

Is there a figure?  If so, I can't see it but we can still talk about the general case.  We know that line BC lies in both planes, ABC and BCE.  If point E also lies in plane ABC, then planes ABC and BCE will be the same.  If point E does not lie in plane ABC, then planes ABC and BCE will be different.  So the answer would seem to be (b) may (be the same plane) depending on the location of point E.