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Two lines parallel to the same plane are parallel to each other?
they are transversals to each others
Are two lines parallel to the same plane parallel to each other?
Not necessarily. They could be skew lines, and satisfy these conditions.
In a plane if two lines are perpendicular to the same line then they are parallel to each other?
Yes they are. It's a postulate: In a plane two lines perpendicular to the same line are parallel.
What are the characteristics of parallel lines?
Parallel lines lying in a plane do not intersect each other. They share exactly zero points in common.
Two lines in a plane are parallel if they cross?
Two lines in a plane are parallel if they do not intersect, meaning they maintain a constant distance between each other and will never meet.
What is the term for lines in a plane that do not intersect?
The term for lines in a plane that do not intersect is "parallel lines." Parallel lines maintain a constant distance from each other and will never meet, regardless of how far they are extended in either direction. In Euclidean geometry, parallel lines exist in the same plane and have the same slope.
Can a pair of lines be both parallel and skew?
No. Parallel has a specific meaning. For lines to be parallel, they have to lie in a common plane, but not touch each other. If they are skew, they still don't touch each other, but they now do not lie in a common plane. More specifically, skew lines, by definition, are not co-planar.
In a plane if two lines are perpendicular to the same line then are they parallel to each other?
So long as all three lines are in the same plane, yes.
If two lines are perpendicular to the same plane then are they parallel to each other?
Yes. [in 3-d].
What does intersecting lines mean?
Intersecting lines are those that lie in the same plane and cross each other at some point. Unless they are parallel, lines in the same plane always cross.
Which geometric object is defined as the set of all points in a plane that are equidistant from each other?
They are parallel lines
Lines cross over each other at a certain point?
In Euclidean geometry, any two lines in a plane that are not parallel will cross.
