I'm not entirely certain what you're asking. Any pair of intersecting lines are of necessity coplanar, (assuming Euclidean geometry) though.
No. The planes must either coincide (they are the same, and intersect everywhere), be parallel (never intersect), or intersect in exactly one line.
2 pairs of parrallel lines
10 One through each pair of vertices, and one through each pair of midpoints - of opposite sides.
1 pair of parallel line
I'm not entirely certain what you're asking. Any pair of intersecting lines are of necessity coplanar, (assuming Euclidean geometry) though.
Yes- planes contain infinitely many points and every pair of points in plane determine a line in that plane, so every plane contains infinitely many lines.
There are an infinite number of planes that pass through a pair of points. Select any plane that passes through both the points and then rotate it along the line joining the two points.
I would say that there are an infinite number of planes that can pass through a pair of skew lines. In order to find the equation of a plane, all you need is three points. take two points off of one line and one point off of the other line and you should be able to derive the equation of a plane. Since the number of points on a line is infinite, an infinite number of planes can be derived.
No. The planes must either coincide (they are the same, and intersect everywhere), be parallel (never intersect), or intersect in exactly one line.
2 pairs of parrallel lines
2 pairs of parallel lines
10 One through each pair of vertices, and one through each pair of midpoints - of opposite sides.
1 pair of parallel line
2
Two.
2