are intersecting lines always coplanar?

Answer 1

Two intersecting lines, L1 and L2, always determine a unique plane. Yes is the answer to your question.

However, If a third line L3 passes through the intersection of L1 and L2 at right angles to both of them, then L1 and L3 form a second plane and L3 and and L2 determine a third plane. But L3 is not coplanar with both L1 and L2. But it is coplanar with L1 and it is also coplanar with L2.

Answer 2

Intersecting Lines Are Coplanar

Answer 3

Sometimes. Look at your walls at home and look at the point where the ceiling and two walls come together. The walls make a line with each other where they intersect and the ceiling makes two lines (one with each of the walls) and they all intersect at the same point. That is an example of three lines that are in different planes (and thus they are not coplanar). Take a sheet of paper and use ruler to draw three lines that intersect in one point. This is an example where all three lines are in one plane and are considered coplanar.

Answer 4

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RE:
are intersecting lines always coplanar?

Answer 5

If it's just two lines intersection, then yes, they are always coplanar. But, if it is more than two, then they don't have to be.

You can demonstrate this with pencils or pens pretty easily.

Answer 6

If you intersect two given lines, then there exists a plane P that contains both lines.

If you intersect *more than* two lines, there there does *not* necessarily exist a plane P containing all 3 lines.

Answer 7

Yes

Answer 8

yes