Of course. The vertices of a triangle, and any three vertices of any other polygon, are non-collinear. In the case of a triangle and a quadrilateral, if you had three collinear vertices, then you couldn't have the polygon.
Collinear points are points that lie on the same line. Noncollinear points do not lie on the same line. Any two points are always collinear, i.e. forming a line. Three or more points can be collinear along a single line.Collinear points lies on the same straight line.
I think you mean: Are any three points contained in exactly one plane? only if they're not collinear... I think
In 3-dimensional space, yes, any three points are coplanar.
== == Through any two points there is exactly one straight line.
just one
Yes. In fact, given any three non-collinear points, there is one (and only one) circle that passes through all three points.
Only one plane can pass through 3 non-collinear points.
Through any three noncollinear points, there is exactly one plane.
Yes a plane can always be drawn three any three points, whether they are linear or not.
No, A plane can be drawn through any 3 points. If the 3 points are collinear then they make a line and a plane can contain a line. If the points are noncollinear then they can be used to form the corners of a triangle; all points of a triangle are in the same plane.
You have to have three or more points to have non-colinear points because any two points determine a line. Noncolinear are NOT on the same line.
Any Euclidean plane has infinitely many points.
No. Any two points can be made to form a line.
Of course. The vertices of a triangle, and any three vertices of any other polygon, are non-collinear. In the case of a triangle and a quadrilateral, if you had three collinear vertices, then you couldn't have the polygon.
Yes. In fact any three points that are not collinear define a plane and therefore MUST lie on a plane.
If you're asking a question, then the answer is 'no'. If you're making a statement, then the statement is false. I can always lay a single plane down on any three points you choose. If your points are in the same straight line, then there an infinite number of other planes that your points all lie in. If they're not all in the same straight line, then there's only one plane.