I'm going thru Geometry basics and I'm stuck just understanding the basics. This doesn't bode well for the year...
Anyway, can someone please explain the following statements:
The statement 'Three points all lie in each of two planes' is true but the statement 'Three noncollinear points all lie in each in each of two planes' is false.
Please explain this. I think of 3 random points. I would think 2 could be in one plane and 1 could be in another plane. Yet Postulate 7 says specifically '... and through any 3 noncollinear points there is exactly one plane.' Why? In my mind I'm still thinking of 3 random points. What is the difference?
Geometry basics?
Details:
Responses (2)
'Three points all lie in each of two planes' means that the three points are co-linear (in one line). It is true because it is possible--it is possible to place three co-linear points in each of two planes.
'Three noncollinear points all lie in each of two planes' is false because the three points are not co-linear (not in one line). It is false because it is impossible--it is impossible to place three non co-linear points in each of two planes.
The question is, what two planes? The answer is two planes which perpendicular to each other.