Creating diagrams using tools
About this video
This video introduces the two classic construction tools: a straight edge for drawing straight lines and a compass for drawing circles. It shows that if you keep the compass opening fixed you can copy circles and line segments exactly, and that two equal arcs centred at A and B can be used to construct the perpendicular bisector of segment AB.
You'll be able to
- describe what a compass and a straight edge are each used for.
- copy a line segment using a compass without measuring it with a ruler.
- explain why every radius of a circle (or of equal circles) has the same length.
- describe how two equal arcs from A and B help construct the perpendicular bisector of AB.
Key words
- compass
- A tool with a pivot point and a pencil that draws circles and arcs of a fixed radius.
- straight edge
- Any tool with a straight side, like a ruler, used to draw straight lines.
- radius
- The distance from the centre of a circle to any point on the circle.
- arc
- A part of a circle.
- perpendicular bisector
- A line that crosses a segment at its midpoint and makes a right angle with it.
Transcript
- [Instructor] So what we're gonna do in this video is get some experience dealing with a compass right over here and a straight edge, sometimes known as a ruler, but it really could be any type of straight edge. And at the simplest level, it's going to help us draw straight lines and circles.
Straight lines with the straight edge. You've probably done something like this before. You can, whoops, I need to be careful not to press buttons. Straight edge, you can just draw a straight line like that. With a compass, you take this pivot point right over here, that should be the center of your circle.
And then this would actually draw your circle, that's where you wanna put a pencil in there. And so here you have it. I am going to keep that pivot point centered, and sometimes you can actually just rotate the paper, but let me just see if I can draw this reasonably well even while the paper slips.
There you go, I have a pretty perfect, pretty perfect circle. Now, what's cool about this, as long as I don't mess with how wide this compass opens, I could draw an identical circle someplace else. I won't even draw the whole thing, but you could imagine I can draw an identical circle.
And I can also use the distance between these two points to make identical line segments. For example, this line segment right over here, let's call this point right over here A, let's call this point right over here B. If I wanna make an identical line segment, what I could do is use, I could obviously measure it with my ruler, but I could also measure it with the compass here.
So now this is the same distance. So if I put some other point here, let's call this A prime. And if I want the same distance from A prime say in that direction, so any line that connects A prime to that little arc that I drew would be the same distance. So just like this, this line that I just drew, I could call this B prime over here, this has the exact same distance as that original segment.
Now there's other interesting things we could do. Let's actually, let's go up here on this AB and let me draw a circle that is centered at A, let me do it like this. Actually, I don't even have to draw the whole circle, let me just do part of the circle right there.
And then I'm gonna keep the radius the same for the circle so I'm not changing my compass, but now I'm gonna draw an arc centered at B, centered at B. Now we'll do more constructions in geometry, but this is already really useful because what we could say is, is that the line, the point that connects these two points, I think we do this in another video, but you might see something interesting if I were to connect that with the straight edge.
In terms of how does it intersect the original segment AB, you might notice that this looks like a right angle, and it is indeed a right angle. And you might look like this distance and this distance is the same if we call this point C, and it is, this is actually a perpendicular bisector, that's one way to construct it and to be pretty precise about it.
Another thing that we can appreciate is the distance between one of these centers and the circle itself, so this distance right over here, let's call this... So that distance right over here, let's call this point D, point D. Any radius is gonna have that same distance.
So if I have this segment right over here, let's call this point E, BE is going to be the same length as BD. And since I kept my protractor, I should say my compass at the exact same length the whole time, these two circles have the same radii as well. So DB would be equal to BE, which would also be equivalent to, let me draw this, whoops.
Which would also be equivalent to, let's call this point F right over here, the length of segment AF. So we'll do more with constructions later, but the big takeaway is with just a straight edge and a compass, there's a lot that you can do to make very precise drawings with circles, have similar angles, and we'll do that kind of thing in the future, have similar or equivalent line lengths, perfect circles, et cetera.
Video © Khan Academy, used under CC BY-NC-SA. Watch on Khan Academy. Puzzicle is not affiliated with Khan Academy.