Hey everyone, it's Justin again. In this lesson we get to go way back in history to
thousands of years ago once again and learn how to construct parallel and perpendicular lines!
By the end of this lesson, you should be able to construct parallel and perpendicular lines
using a compass and straight edge. First, we'll define parallel and perpendicular.
Next, we'll learn one way to construct parallel lines and then
we'll learn another way to construct perpendicular lines. Grab your straightedge
and compass again for this lesson and tuck that ruler away. Let's get started.
So what do parallel and perpendicular mean? You're probably familiar with these terms from
your previous math courses but let's refresh our memory. Two lines that are parallel must
be on the same plane but never intersect. In this example, lines LM and CB are parallel.
This symbol means parallel and on the sketch itself we can tell people that the lines are
parallel by using this little arrow symbol. Then there's perpendicular. Perpendicular lines
are also on the same plane as each other but do intersect and more specifically,
they intersect at a right or 90 degree angle. In this example, lines NP and DE are perpendicular.
This symbol is used for perpendicular when writing this out and this symbol is used for perpendicular
on a drawing. It looks like we're putting a little square in one of the right angles and since there
are four right angles here, you could put this symbol in any of them. Pause the video here if
you need more time to write your notes for this. Next up we're gonna start some constructions.
We're going to learn one way to construct parallel lines together
and then you'll have an opportunity to explore two more ways in your activity later on.
The method we're using is the angle copy method. It'll be best to create this in your notes as we
go so remember to pause the video anytime you need to catch up or re-watch something.
Start by drawing a line like this. Then use your straight edge to draw a segment going through
that line that you can tell is definitely not perpendicular to the original line.
Place a point on this new segment that you would like your parallel line to go through.
Set a distance on your compass that's not too big and draw an arc where the line
and segment intersect. Go up to the new point you made and draw the same arc there too.
Then, set the distance on your compass where the arc meets up with both your line and segment.
Copy that distance up on your other arc using that same compass setting.
Point R in the intersection you just created with your compass is where you'll draw the parallel
line. We can make all of our compass marks a little lighter if we want to by gently erasing it
so that it's easier to see the parallel lines. We can mark them as parallel and if we put two points
somewhere anywhere on each line then we can also write a description of what our picture shows.
There's some space in your notes template to practice this one more time before we move on
so pause the video now and resume when you're ready to learn about a perpendicular construction.
Next, we are going to go over a method for finding a perpendicular line and actually
more specifically, the perpendicular bisector. We learned what perpendicular means earlier,
but do you know what bisect means? Bisect means splitting something into two
equal parts. You'll see two other methods in your lesson activity for finding a perpendicular line
but I figured we could look at this more specific perpendicular bisector case
together. Remember how a line goes on forever and ever in both directions? So how do you bisect
or split something in half something that technically doesn't have a middle? You don't,
which is why we're going to bisect a line segment here instead of a line.
Okay, let's get started. Draw a segment and set your compass so that it's definitely longer than
halfway across the segment, but not entirely the way across. Use this setting to draw an arc
above and below the segment. Move the compass tip to the other end point of the segment and
be sure that the setting doesn't change. Draw two more arcs just like what you did before.
The two places that the arcs intersect each other are actually the two places we need to
draw our new line through. You could just draw a segment here but I'm going to keep the arrows
on the ends of this so that it's a line. We weren't told in the directions that we have
to write the notation for this but it's good practice so let's label some points. On the
segment we have to use the endpoints, but on the line remember that our points can be anywhere.
You also don't have to use the same letters as me, that's totally up to you. Now we can write
the notation for this. This says that line SH is perpendicular to segment FI. And don't be afraid
to write your answer in different ways, here's a few of the many more ways you can write this. We
can also put in a little box in one of the corners to show that we have right angles in our drawing.
There's one other thing I haven't shown you yet. Remember that I said we weren't just
making a perpendicular line in this construction but we were also bisecting segment FI? Well that
means segment FH and segment HI are congruent to each other. You may as well write that down too
and put a little congruent symbol on our drawing to show that. Also if you want to lighten up your
compass markings now's a good time to do that too. All right, that's the end of our perpendicular
example. Pause the video now and try to make this one more time in your notes all by yourself.
There are two more ways to find a perpendicular line that you'll have a chance to explore in your
activity for this lesson and these other ways don't require that you start with a segment,
you can start with a line instead. Now that you've explored ways to construct parallel
and perpendicular lines, I hope you're getting comfortable with your compass and straight edge.
Once you finish your activity for this lesson, we're going to advance to some other concepts
using line segments that were more recently developed in history. See you next time!