Q: If two lines are parallel to the same line then they are to each other?

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No

They are parallel to each other.

Yes.

the parallel lines never intersect each other but they both intersect the line they are perpendicular to

No, "y" is not a parallel line because the lines are not perpendicular to each other. "Y" is a skew line.

Related questions

They are parallel to each other.

E does have parallel lines. The three line are parallel to each other

If two lines are parallel to the same line, then they are parallel to each other.

If two lines are parallel to the same line, then they are parallel to each other.

No

They are parallel to each other.

Yes.

the parallel lines never intersect each other but they both intersect the line they are perpendicular to

A square and a rectangle have perpendicular and parallel lines. The two side lines extending upwards from the base line are perpendicular to the base line. The line extending from each of the side lines across the top is perpendicular to the side lines. The top line is also parallel to the base line, and the side lines are also parallel to each other.

No, "y" is not a parallel line because the lines are not perpendicular to each other. "Y" is a skew line.

A square and a rectangle have perpendicular and parallel lines. The two side lines extending upwards from the base line are perpendicular to the base line. The line extending from each of the side lines across the top is perpendicular to the side lines. The top line is also parallel to the base line, and the side lines are also parallel to each other.

Parallel lines run in the same direction. If they are intersected by one line and that line is perpendicular to both, then it proves that the lines run parallel to each other.