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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.
If two lines lie in the same plane and have more than on point in common they must be?
the same line
If two lines lie in the same plane and have more than one point in common they must be?
Identical.
Is 3 points coplanar colinear?
3 coplanar points may or may not be collinear. 3 collinear points must be coplanar.
Are points of a circle coplanar?
Yes. A circle is defined as the set of all points in a plane equidistant from a given point (the center of the circle) - hence - all points of a circle must be co-planar by definition.
What are two coplanar lines called that have no points in common?
Coplanar lines that do not intersect (have no common point) are parallel.Two objects are coplanar if they both lie in the same plane, they must either intersect or be parallel.
Is a ray an example of an angle?
NO An angle is comprised of two rays, lines, or line segments. The two being used must come from the point point in space and must be coplanar. (It must be to lines coming from the same point.)
If two lines are not coplanar then they are neither intersecting nor parallel?
CorrectParallel lines as well as intersecting lines must be coplanar (in Euclidean geometry not quite sure about hyperbolic geometry...).Lines in space which neither are coplanar nor intersecting are called "skew"
Two lines which intersect to form right angles?
...must be coplanar.
True or false If two lines are coplanar then they must touch?
false
If two lines are coplanar then they must touch?
No. If they are parallel (but not identical), they will not touch.
If two coplanar lines do not intersect then they must be what?
Skew. * * * * * FALSE. In fact, if they are skew, they must intersect. They have to be parallel for them not to intersect.
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.
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.
If two lines lie in the same plane and have more than on point in common they must be?
the same line
If two lines lie in the same plane and have more than one point in common they must be?
Identical.
What two lines are coplanar?
Two lines are coplanar if they both have 2 points in the same plane. So in an X,Y,Z grid, one slope, be it X Y or Z, must be the same for both lines. To find the slope, use Y1-Y2/X1-X2 or replace one of those values with Z. For this particular example, it doesn't matter which is on the numerator, because it is a comparison. ================================ Short-cut: Two lines that intersect are always coplanar.
