Question

What is the difference between intersecting and perpendicular lines? Can two lines exist that are not intersecting or parallel? Explain your answer.

Answer 1

Perpencidular lines must intersect but not all intersecting lines are perpendicular
Perpendicular lines cross at the point at which they form their 90 degree angles.
But two intersect lines can cross without forming a 90 degree angle.
For example, imagine two toothpicks on top of each other. Do they always form 90 degree angles?

Two lines can, in fact, exist which are neither parallel nor intersecting.
In dimensions higher than two, there’s this idea of “skew” lines.

For example, imagine a line drawn along the middle of your ceiling.
Then imagine another random line drawn along the wall.
They’ll most likely not intersect. And they’re not what you would call parallel either.
So we call them “skew lines” in the sense that although they never intersect, they really aren’t going in the same direction either.

Also, on a plane, two lines might actually turn out to be the same line.
I don’t think they’d be labeled as intersecting or parallel lines since they’re the same lines.
For example 3x + 4y = 10 and 28y = 70 – 21x turn out to be the same line.