Lesson video

Hello, and welcome to this lesson on angle bisectors.

Now, before you start this lesson, you're going to need a pen or pencil, a ruler and a protractor.

Remember, protractor is something used to measure angle's width.

Make sure you get those things before you carry on with today's lesson.

Okay, now that you have those things, my name is Mr. Maseko, let's get on with today's lesson.

Firstly, try this activity.

So take a piece of paper, and what you're going to do is mark two adjacent line segments, AB and AC.

And what you're going to do is you're going to make this angle as shown here.

So the angle can be any size you want.

And what you're going to do is you're going to measure that angle, and then you're going to fold your piece of paper, so the line segments AB and AC overlap.

And what do you notice when you do that? Pause the video here and give this a go.

Okay, now that you've tried this, let's see what you should've noticed.

Well, you should've noticed that when you folded your piece of paper, so the line segments AB and AC overlapped, you should've noticed that those two angles were exactly half the overall angle.

So that fold line in the middle, that fold line was your angle bisector.

And we talked about bisectors in the last lesson, but were talking about perpendicular bisectors in the last lesson, but now we're talking about angle bisectors.

So align that card and angle exactly in half.

Now, another thing that I want you to try is this.

So, mark two points on the lines AB and AC, and measure the distance of those points to the fold line.

What do you notice? Pause the video here and give that a go.

Okay, now that you've tried this, let's see what you have noticed.

Well, just like those two angles were the same when you measured them, and they were half the size of angle BAC, wat you should have noticed is that distance from the point that you marked to the fold line was exactly the same.

So that fold line, that fold line was our angle bisector because it cut our angle in half.

That angle bisector, a proper definition for that line would be, here it is.

An angle bisector is a locus of points that are equidistant between two line segments.

Make sure you write this down and compare it with our definition for a perpendicular bisector.

So remember, based with last lesson, we said a perpendicular bisector is a locus of points that are equidistant from two points.

So angle bisector, on the other hand, is a locus of points that are equidistant between two line segments.

So not two points, but rather two line segments.

And whatever point you pick on lines AB and AC, you should notice the distance from those points to the fold line, which is your angle bisector, is exactly the same.

Like locus of points is equidistant between those two line segments.

Now, here we have instructions of what to do when we want to bisect and angle.

And these are the instructions we're going to follow each time.

So what you're going to do is you're going to create two points that we've just done, where you created two points that are equidistant from point A.

So point A is what the centre of your angle.

So those two points has through the same distance from point A.

And then, what you're going to do is join those two points with the straight line, and then mark the midpoint of that line, and then you're going to join that to point A, and that is your angle bisector.

Okay? So let's practise this.

Draw the following angles accurately.

So you're going to draw a straight line that measure an angle of 40 degrees.

Draw a straight line measure an angle of 20 degrees.

Draw a straight line and measure an angle of 80 degrees.

And then bisect them using the instructions that we've just talked about.

Pause the video here and give that a go.

Okay, now that you've tried this, let's see what you should have come up with.

Well, you should have picked two points on the line AB and AC that are the same distance from AC.

I've used a ruler to measure this.

And then, join those two points with a straight line, and then marks the midpoint of the line.

We can measure that with a ruler.

And then, if you join that to point A, and you've now constructed your angle bisector.

So you've done the same thing with all these angles, midpoint, and then the ruler.

Yours will be much neater than mine 'cause you'll be using a ruler, and it, you would have measured all these distances accurately.

But the most important thing is that the distance from point A to the points that you've picked is the same on both lines, otherwise, you won't have an angle bisector.

Like, let me show you what this would look like if those distance were different.

So if I did this point here, and then we'll say picks that point there, you can see clearly that these two distances are not the same.

Now, if I join those with a straight line, and mark the midpoint, it's very easy to see that that's not the angle bisector because this side of the angle is not the same as that side of the angle.

That's why those two points that you make have to be the same distance from the central point of your angle.

So this explore task, a little bit practising doing those angle bisectors a lot more.

Now, draw a large triangle and label the vertices ABC, and then bisect each of those angles, and see what you notice.

Pause the video here and give this a go.

Okay, now that you've tried this, let's see what should happen.

Well, if your bisector angled against C, pick two points, join them with the straight line, mark the midpoint, bisect, same thing for all the angles, straight line, bisect, two points, straight line, midpoint, and then bisect.

What you notice is that those three angle bisectors meet at a point, so a single point.

And that single point turns out to be as centre.

So a type of centre for this triangle.

Now, will other triangles all find the same centre? Or draw different triangles and see if you find a centre for that triangle.

So will this always work? If you want to share all other triangles that you've tried, ask your parent or carer to share work on Twitter, tagging @OakNational and #LearnwithOAk.