Parallel and perpendicular
Let's think a little bit about two terms that you'll see throughout your geometry, and really, mathematical career. One is the idea of things being perpendicular. And usually, people are talking about perpendicular. Actually I'm misspelling it-- perpendicular lines, and the idea of parallel lines. So perpendicular lines are two lines that intersect at a right angle. So what am I talking about? So let's say that this is one line right over here and that this is another line right over here. We would say these two lines are perpendicular if they intersect at a right angle. So they clearly intersect. In order for them to intersect at a right angle, the angle formed between these two lines needs to be 90 degrees. And if any one of these angles is 90 degrees, the rest of them are going to be 90 degrees. So this is 90 degrees, then these are perpendicular lines. And if that's 90 degrees, then that's going to be 90 degrees, that's going to be 90 degrees, and that's going to be 90 degrees. So if any of them are 90 degrees, the rest of them are 90 degrees, and we have perpendicular lines. If you have two lines that on a two-dimensional surface like your paper or like the screen never intersect, they stay the same distance apart, then we are talking about parallel lines. So this line right over here and this line right over here, the way I've drawn them, are parallel lines. They aren't intersecting. They're both kind of going in the same direction, but they're kind of shifted versions of each other. They will never intersect with each other. So these two are parallel. If we have two lines that, let's say, they intersect, but they don't intersect at a right angle, so let's say we have that line and we have this line right over here, and they're clearly not intersecting at a right angle, then we call these neither perpendicular nor parallel lines. These lines just intersect.