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they lie in the same plane
Albert Roberts
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A line that intersects two coplanar lines at two distinct points is called what?
transversal
What does it mean for two points to be coplanar?
If two points are coplanar, they lie on the same plane.
Four points are always co planar if?
They are coplanar if the line joining any two of them intersects the line joining the other two.
What are non-coplanar lines?
In Euclidean Geometry, two non-coplanar lines are two lines in 3-dimensional space for which no single plane contains allpoints in both lines. For any two lines in three dimensional space, there is always at least one plane that contains all points in one line and at least one point in the other line. But there is not always (in fact it's quite rare) that any plane will contain all points in both lines. When it happens, there is only one such plane for any two distinct lines. Note that, any two lines in 3-dimensional space that intersect each other mustbe coplanar. Also, any two lines in 3-dimensional space that are parallel to each other must also be coplanar. So, in order to be non-coplanar, two lines in 3-dimensional space must a) not intersect each other at any point, and b) not be parallel to each other. (As it turns out, this dual condition is not only necessary, but sufficient for non-coplanarity.) Also note that, as a test for coplanarity of two lines, you need only test two points on each line, for a total of four points, because all points on a single line are, by definition, on the same plane. In fact, all you really have to do is test a single point on one line against three other points (one on the same line and two on the other line), because, by definition, any three points in 3-dimensional space are on the same plane. For example, consider any two distinct points on line m (A and B), and any two distinct points on line l (C and D). Points A and B are obviously coplanar because they are colinear (in fact, they are coplanar in the infinite number of planes that contain this line). Point C on line l is also coplanar with points A and B, because by definition, any 3 non-colinear points in 3-dimensional space define a plane (however, if point C is not on line m, the number of planes that contain all three points is immediately reduced from infinity to one). So the coplanarity test for the first three points is trivial - they are coplanar no matter what. However, it is not at all certain that point D will be on the same plane as points A, B, and C. In fact, for any two random lines in 3-dimensional space, the probability that the four points (two on each line) are coplanar is inifinitesimally small. But, if the fourth point, the one not used to define the plane, is nevertheless coplanar with the three points that define the plane, then lines l and m are coplanar. Note that, though I specified that points A and B on line m must be distinct, and that points C and D on line l must be distinct, I did not specify that C and D must both be distinct from both A and B. That is because, if, for example, A and C are the same (not distinct) point, then, obviously, lines m and l intersect, at point A, which is the same as point C. If this is the case, then the question of whether D is on the same plane as A, B, and C is trivial, because you really only have 3 distinct points, and any three distinct points alwaysshare a plane. That is why intersecting lines (lines that share a single point) are always coplanar. But you're asking about non-coplanar lines. So, basically, if any point on either of the two lines is not coplanar with the other three points (one on the same line and two on the other line), then the lines are non-coplanar.
Where do coplanar points lie on?
Coplanar points lie on the same plane. A plane is a flat, two-dimensional surface that extends infinitely in all directions. Coplanar points can be thought of as points that all lie in the same plane and can be connected by straight lines without leaving that plane.
What are the three points for coplanar but not collinear?
Two points (which must lie on a line) and the third point NOT on that line.
A line that intersects two coplanar lines at two different points?
Transversal
What is coplanar points?
Definition of Coplanar points: Coplanar means that the points are on the equal plane. Plane is a two-dimensional object, with as such is a bit more complicated.Collinear,line,plane and point are the related terms of coplanar.Points that are on the same plane. 2 points are alwayscoplanar...3 points are always coplanar...4 points are sometimes coplanar.
A line that intersects two coplanar lines at two distinct points is called what?
transversal
What is a line that intersects two or more coplanar lines at different points?
It is a tranversal.
Are any two points coplanar?
Yes. Any two points are always coplanar.
What does it mean for two points to be coplanar?
If two points are coplanar, they lie on the same plane.
Four points are always co planar if?
They are coplanar if the line joining any two of them intersects the line joining the other two.
A line and two points are guaranteed to be coplanar if?
they lie in the same plane
Line that intersects two coplanar lines at different points?
Think of an H one line intersects two others, this is called transversal
What is the definition of coplanar points?
>Two points that lie on the same plane. Any pair of points on the plane will thus >form a line. (In most basic geometry classes, the majority of the class work is >only concerned with one plane) Any number of points can be coplanar. In fact, any 3 points are always coplanar, and if they are not colinear (all three on the same line), they define a unique plane.
Are three points always collinear?
No but they are always coplanar.
