Geometric constructions: perpendicular bisector
About this video
The video constructs the perpendicular bisector of segment AB with a virtual compass and straight edge. Two circles with radius AB are drawn, one centred at A and one at B, and the line through their two intersection points is the perpendicular bisector.
You'll be able to
- explain what a perpendicular bisector is.
- construct a perpendicular bisector using two circles and a straight edge.
Key words
- perpendicular bisector
- A line that crosses a segment at its midpoint and makes a 90-degree angle with it.
- bisect
- To cut into two equal parts.
- compass
- A tool that draws a circle of a chosen radius around a centre point.
Transcript
We're asked to construct a perpendicular bisector of the line segment AB. So the fact that it's perpendicular means that this line will make a 90-degree angle where it intersects with AB. And it's going to bisect it, so it's going to go halfway in between. And I have at my disposal some tools I can put out.
I can draw things with a compass, and I can add a straight edge. So let's try this out. So let me add a compass. And so this is a virtual compass. So in a real compass, it's one of those little metal things where you can pivot it on one point, and you can draw a circle of any radius.
And so here I'm going to draw-- I'm going to center it at A. And I'm going to make the radius equal to the length of AB. Now I'm going to add another circle with my compass. And now, I'm going to center it at B and make the radius equal to AB. And now, this gives me two points that I can actually use to draw my perpendicular bisector.
If I connected this point and this point, it is going to bisect AB, and it's also going to be perpendicular. So let's add a straight edge here, so this is to draw a line. So I'm going to draw a line between that point and that point right over there. And let me scroll down, so you can look at it a little bit clearer.
So there you go. That's my construction. I've made a perpendicular bisector for segment AB. Check my answer. We got it right.
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