Q: Do three lines that intersect at the same point have to be at the same plane?

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collinear plane

It's possible, but for any three lines in the same plane, there could be ether one point of intersection (unlikely) or three (more probably).

Yes, in Euclidean geometry, an infinite number of lines can meet at one point.

A triangle? Three lines that intersect in three points.

Yes (assuming all three lines are in the same plane).

Related questions

collinear plane

no

It's possible, but for any three lines in the same plane, there could be ether one point of intersection (unlikely) or three (more probably).

No, only three lines can intersect at a single point.

No. Any pair of the three will describe a plane, so the three possible pairs describe three planes.

its the point of concurrency

concurrent lines

concurrent

Three or more straight lines in a plane such that they intersect pairwise.

Any number of lines can intersect all at the same point. Think of a circle. Now think of all of its diameters.

Yes, in Euclidean geometry, an infinite number of lines can meet at one point.

No. If they are parallel, then a plane exists which both lines lie in. Skew lines can not be on the same plane.