Learn about Lines and Planes

In this lesson, let’s learn about lines and planes. The problem given to us wants us to identify the parallel, perpendicular and skew lines in the figure given below. And we also need to identify the parallel planes. Well, before we start let’s understand what are parallel lines. Parallel lines are lines that are—that will never intersect. Parallel lines are on the same plane I’m going to show you this with the examples. They’re on the same plane but they never intersect. Perpendicular lines are on the same plane but they intersect at 90 degree angles. And skew lines are not on the same plane. Now, that we understood all three definitions let’s try to identify them. Let’s try parallel lines which is parallel lines are lines that on the same plane but never intersect.

So this for example, the square is a plane it’s a flat surface which are the lines that never intersect. If I look at the line AE, this is how we represent line AE the two endpoints and DH are called parallel lines these are the symbol for parallel because A and E and D and H no matter how far we extend it they will never intersect. Similarly we have EH and AD, AD is parallel to EH. Those are the two parallel sets of lines on this plane. Similarly if we look at this plane which is DCGH we’ll have DC will be parallel to—DC is here, this is parallel to GH or HG. Similarly CG is parallel to DH. We’re considering this plane. So this and this are parallel, this and this are parallel and you get the idea. So this is parallel to this, this is parallel to this, this is parallel to this, this is parallel to this and so on. So with each surface having two sets there will be many, many sets of parallel lines for this particular cube.

Now, let’s look and I’m going to erase the markings that I did. Now, let’s understand perpendicular lines, these are parallel. Now, let’s understand perpendicular lines. Perpendicular lines always intersect but they are—perpendicular lines intersect at 90 degrees. So if we look at the first plane, let’s take this plane as an example. This angle is 90 degrees, this angle is 90 degrees, this is 90 degrees and this is 90 degrees so this line and this line are perpendicular which means D and H—this is a symbol for perpendicular D and H is perpendicular to HG, D and H is also perpendicular to DC. You get the idea? This line is perpendicular, this one and this one because this and this intersect at right angles, this and this intersect at 90 degrees so similarly this and this are right angles. So let’s say CG is perpendicular to GH, CG is also perpendicular to DC. You get the idea? There’s many more.

That’s how we manage to identify the perpendicular lines. Now, the next is skew lines. Skew lines are not on the same plane so let’s take one line on one plane, another line on another plane these two skew. So skew lines are EF and DH for example are skew. Similarly CG and I can take any other plane. Let’s take this plane. So this is going this way, this is going to this way because they’re on different planes, they’ll never intersect. So CG skew with EH, you get the idea? So that’s—there are many more and you can practice that yourself for the idea about skew lines is they’re not on the same plane. If they’re not on the same plane they will never be parallel or intersecting because it’s like lines at two different planes.

The only other thing we have to do is identify the parallel planes. Parallel planes never intersect. This is one plane and this is a plane parallel to it. So if I want to do parallel planes, what are they? So ADHE is parallel to the bottom plane which is BFGC. As you can see this plane and this plane no matter how far we extend it they will never intersect. Key things that we’ve learned, parallel lines never intersect but they must be on the same plane. Perpendicular lines always intersect at 90 degrees these are perpendicular, this is perpendicular to this, this is perpendicular to this and so on. Skew lines never—are on the same plane and parallel planes are like parallel lines. Two different planes that are parallel to each other which means they never intersect.