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Is it true without exception that if P Q R are points contained by plane X and also by plane Y then X is the same plane as Y?
No.
If the points are all in a straight line, then they could lie along the line of intersection of both planes.
Mark three points on a piece of paper, in a straight line, and then fold the paper along that line so that the paper makes two intersecting planes. The three points on on each plane, but the plants are not the same.
What else can I help you with?
If points F and G are contained in a plane then is entirely contained in that plane?
Is true
If points P and Q are contained in a plane the PQ is entirely contained in that plane?
Yes, if points P and Q are contained in a plane, then the line segment connecting P and Q, denoted as PQ, is also entirely contained in that plane. This is a fundamental property of planes in Euclidean geometry, where any line segment formed by two points within the same plane must lie entirely within that plane. Therefore, the assertion is correct.
Can three noncollinear points be contained on one plane?
Yes. You require three non-collinear points to uniquely define a plane!
What is the least number of points that cannot be contained in just one plane?
7,975
Is it true that three points are always contained in exactly one plane?
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.
If points P and Q are contained in a plane then is entirely contained in that plane.?
True.
If points F and G are contained in a plane then is entirely contained in that plane?
Is true
If points F and G are contained in a plane then is entirely contained in that plane.?
Is true
If points R and S are contained in a plane then is entirely contained in that plane.?
True!
If points r and s are contained in a plane then rs is entirely contained in that plane?
It’s true (apex)
If points p and q are contained in a plane then pq is entirely contained in that plane?
true
Can three noncollinear points be contained on one plane?
Yes. You require three non-collinear points to uniquely define a plane!
If points f and g are contained in a plane then fg is entirely contained in that?
Is true
Any two points are contained in exactly one plane?
false
What is the least number of points that cannot be contained in just one plane?
7,975
Is it true that three points are always contained in exactly one plane?
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.
Are three noncollinear points always contained in only one plane?
Yes a plane can always be drawn three any three points, whether they are linear or not.
