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If two lines intersect then they intersect in exactly one what?
If two lines intersect, they intersect in exactly one point. This point is the location where the two lines cross each other in a two-dimensional plane. In Euclidean geometry, two distinct lines can either intersect at one point or be parallel, in which case they do not intersect at all.
When two or more lines intersect at a point they are said to be?
Theorem: If two lines intersect, then exactly one plane contains both lines. So, when two or more lines intersect at one point, they lie exactly in the same plane. When two or more lines intersect at one point, their point of intersection satisfies all equations of those lines. In other words, the equations of these lines have the same solution, which is the point of intersection.
How many Counterexamples are needed to disprove the conjecture two lines in a plane always intersect at exactly one point?
To disprove the conjecture that two lines in a plane always intersect at exactly one point, only one counterexample is needed. A single example of two lines that do not intersect, such as two parallel lines, is sufficient to show that the conjecture is false. Therefore, one counterexample is enough to invalidate the claim.
If two lines intersect then they lie in one plane. Is this true always sometimes or never?
always. if two lines intersect, then exactly one plane contains the lines.
When does a plane and line intersect at one point?
When the line is inclined to the plane. That is, it is not in the plane nor is it parallel to it.
If two planes intersect do they intersect in exactly one plane?
No, two planes do not intersect in exactly one plane unless the planes are exactly overlapping, making one plane. In Euclidean Geometry two planes intersect in exactly one line.
If two lines intersect then they intersect in exactly one what?
If two lines intersect, they intersect in exactly one point. This point is the location where the two lines cross each other in a two-dimensional plane. In Euclidean geometry, two distinct lines can either intersect at one point or be parallel, in which case they do not intersect at all.
Two planes can intersect on exactly one point?
No, 2 planes may only intersect at a line, a plane, or not at all. THREE planes may intersect at a point though...
When two or more lines intersect at a point they are said to be?
Theorem: If two lines intersect, then exactly one plane contains both lines. So, when two or more lines intersect at one point, they lie exactly in the same plane. When two or more lines intersect at one point, their point of intersection satisfies all equations of those lines. In other words, the equations of these lines have the same solution, which is the point of intersection.
Three planes may all intersect each other at exactly one point?
Three planes may all intersect each other at exactly one point. This commonly occurs when there is one straight plane and two other planes intersect it at acute or obtuse angles.
How many Counterexamples are needed to disprove the conjecture two lines in a plane always intersect at exactly one point?
To disprove the conjecture that two lines in a plane always intersect at exactly one point, only one counterexample is needed. A single example of two lines that do not intersect, such as two parallel lines, is sufficient to show that the conjecture is false. Therefore, one counterexample is enough to invalidate the claim.
To cross at exactly one point?
To intersect.
What is a tangent internally?
Two circles in the same plane are externally tangent if they intersect in exactly one point and their intersection of their interiors is empty.
A plane and a line intersect at most in one point?
Yes, except when the line is in the plane. In the latter case, they intersect at each point on the line (an infinite number).
If two lines intersect then they lie in one plane. Is this true always sometimes or never?
always. if two lines intersect, then exactly one plane contains the lines.
When does a plane and line intersect at one point?
When the line is inclined to the plane. That is, it is not in the plane nor is it parallel to it.
The point at which a line and a circle intersect at exactly one point?
Tangent
