Question

Two parallel lines are _____ coplanar.

never


sometimes


always


Two lines that lie in parallel planes are _____ parallel.


sometimes


always


never



Please explain the answers, I want to understand this better.

Answer 1

always

sometimes

Explanation:

By definition parallel lines are lines in a plane which do not meet, that means, they have to be coplanar. Coplanar means they are included in the same plane. Then, two parallel lines are always coplanar (imagine two parallel lines in a 3d space, there is always a plane that can contain them).

Two lines that lie in parallel planes are sometimes parallel. As stated before, if there is a third plane which contains the two lines, they can be parallel or cannot, but if there is no plane which contains them, they are not parallel.

Answer 2

1. always

2. sometimes

Explanation:

Two lines are coplanar if they lie in the same plane or in parallel planes. There is ALWAYS a plane which contains two parallel lines (see first attached image for details).

Two lines that lie in parallel planes are sometimes parallel. For example, see at second image. Planes
`\alpha` and
`\beta` are parallel. Consider pair of lines
`a` and
`a_1` - they are parallel, but if you consider the pair of lines
`a` and
`b_1`, you can see they are not parallel.