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True or false three lines that intersect at the same point must all be in the same plane and why?
False. Think of a corner of a cube such as a room. If you face the corner, there is one line defined by the floor and the wall to your left. A second line defined by the floor and wall to your right and the third line, going vertically, defined by the two walls. These three lines are mutually perpendicualr (or orthogonal) - very definitely not coplanar.
What else can I help you with?
Plane has two number lines that intersect at the point called the?
false.
What is a counterexample to this conjecture if three lines lie in the same plane then they intersect in at least one point?
A counterexample to the conjecture is when three parallel lines lie in the same plane. In this case, none of the lines intersect at any point, demonstrating that it is possible for three lines in the same plane to not intersect at all. Therefore, the conjecture is proven false.
What parallel lines intersect?
Parallel lines in the Euclidean plane do not intersect but all parallel lines in the projective plane intersect at the point at infinity.
Will non parallel lines intersect?
If the 2 lines lie in the same plane, and they are not parallel, then they will intersect at some point. If the 2 lines are skew lines, then they are not in the same plane, and they will not intersect (but they are Not Parallel)
Do skew lines intersect if they are in the same plane?
No, skew lines cannot be in the same plane, since they do not have a point on common. Two lines intersect if they lie in a common plane, and by definition, these intersecting lines are not skew lines.
Plane has two number lines that intersect at the point called the?
false.
Can the lines of a plane intersect?
All non-parallel lines in a plane will intersect at some point in the plane.
What is a counterexample to this conjecture if three lines lie in the same plane then they intersect in at least one point?
A counterexample to the conjecture is when three parallel lines lie in the same plane. In this case, none of the lines intersect at any point, demonstrating that it is possible for three lines in the same plane to not intersect at all. Therefore, the conjecture is proven false.
What parallel lines intersect?
Parallel lines in the Euclidean plane do not intersect but all parallel lines in the projective plane intersect at the point at infinity.
If two lines intersect they intersect in an infinite number of ponits true or false?
false they intersect at a single point
Will non parallel lines intersect?
If the 2 lines lie in the same plane, and they are not parallel, then they will intersect at some point. If the 2 lines are skew lines, then they are not in the same plane, and they will not intersect (but they are Not Parallel)
Do skew lines intersect if they are in the same plane?
No, skew lines cannot be in the same plane, since they do not have a point on common. Two lines intersect if they lie in a common plane, and by definition, these intersecting lines are not skew lines.
If two lines intersect they intersect in an infinite number of points true or false?
False. If two lines intersect, they do so at exactly one point, provided they are not parallel. In Euclidean geometry, two distinct lines can either intersect at a single point or be parallel and never intersect at all.
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.
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 lines that intersect in a point but do not all lie in the same plane?
collinear plane
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.
