Q: What would you call two lines which do not intersect?

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Two lines that intersect and form 90-degree angles (right angles) are "perpendicular" to each other. You would call them "perpendicular lines."

Parallel lines.

skewed lines

Vertex

Two lines that are equidistant and, therefore, never intersect, would be parallel lines.

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Two lines that intersect and form 90-degree angles (right angles) are "perpendicular" to each other. You would call them "perpendicular lines."

Skew lines.

Parallel lines.

skewed lines

The intercept

Vertex

Two lines that are equidistant and, therefore, never intersect, would be parallel lines.

They do not. A set of lines can also be considered as a system of linear equations. But the fact that there is such a system does not mean that the lines intersect.

Two lines intersect at a point

The lines that intersect to Form A right triangle are called Perpendicular Lines; the resulting meeting point of these two lines is called the vertex of the angle.

Parallel lines do not intersect.

Two lines that do not intersect on the same plane are Parallel lines.