Three points determine exactly one plane.
That means that if you bring me a plane, then some or all of my three points may or
may not lie in your plane. But if you bring me three points, then I can always draw a
plane in which all of your points lie, and I can also guarantee that it's the only one.
By the way ... three points also determine exactly one circle.
false
I think you mean: Are any three points contained in exactly one plane? only if they're not collinear... I think
True.
Is true
True!
3 points must always be contained in one plane, as 2 make a line, it makes no difference as to where the third point is, it will exist in the same plane in the two. Aside from all three points being in a line, this is always true.
Yes, three non-collinear points are contained in exactly one plane. By definition, non-collinear points do not all lie on the same straight line, which allows them to define a unique plane. In geometry, any three points that are not collinear will always determine a single plane in which they lie.
false
I think you mean: Are any three points contained in exactly one plane? only if they're not collinear... I think
Yes a plane can always be drawn three any three points, whether they are linear or not.
Yes, if you are talking about Euclidean geometry.
True.
Is true
Is true
True!
If points p and q are contained in a plane, then the line segment connecting p and q also lies entirely within that plane. In Euclidean geometry, any two points define a straight line, and since both points are in the same plane, the entire line segment joining them must also be contained in that plane. Therefore, it is accurate to say that points p and q, along with all points between them, are entirely contained in the plane.
It’s true (apex)