Two lines are parallel in space if they are coplanar and do not intersect.
How can you determine if a line is parallel to a plane?
A line is parallel to a plane if it does not intersect the plane.
What is the parallel postulate in geometry?
The parallel postulate states that through a point not on a line, there is exactly one line parallel to the given line.
How can you prove two planes are parallel?
Two planes are parallel if they do not intersect, which can be shown if corresponding lines within the planes are parallel.
What is the symbol for parallel lines?
The symbol for parallel lines is '||'.
Can a line be parallel to two planes at the same time?
Yes, a line can be parallel to two planes if it is not intersecting either plane.
What is a transversal line?
A transversal line is a line that intersects two or more lines at distinct points.
How do parallel lines behave in Euclidean geometry compared to non-Euclidean geometry?
In Euclidean geometry, parallel lines never meet. In non-Euclidean geometry, the concept can differ, such as in hyperbolic geometry where lines may diverge.
What is the relationship between skew lines and parallelism?
Skew lines are non-coplanar lines that do not intersect and are not parallel.
Can planes that intersect be parallel?
No, planes that intersect cannot be parallel as they meet at a line.
What is the relationship between parallel planes and lines?
If two planes are parallel, then a line perpendicular to one plane is also perpendicular to the other plane.
What is a real-world example of parallel planes?
The floors of a two-story building represent parallel planes.
What is the effect of parallelism on angles formed by a transversal line?
If a transversal cuts parallel lines, it creates corresponding angles that are equal.
How do you represent a plane parallel to a line in notation?
You can represent a line 'l' parallel to plane 'P' as l || P.
What geometric tool can you use to check for parallelism in 3D models?
A protractor or parallel line indicator can be used along with visual inspection to check parallelism in models.