In this video, I will show you a technique for dividing any segment into an arbitrary number of equal pieces. The advantage of this technique of course is its arbitrariness, you can divide it into any number of segments that you want. The disadvantage is its complexity. Once you understand the idea, though, the procedure is fairly straightforward. So I have a segment A B here that I'd like to divide into, let's say five equal parts. We begin by drawing a line from a at some arbitrary angle.
And then draw a circle from a at some arbitrary size. I'll label this point C. Add additional circles, according to the number of divisions that you want. So I'll draw a circle from C to A and then repeat that making equal sized circles Now I'm going to label these points, D, E, F, and G. So now we have five equal segments going up the line, we need to transpose this information onto our segment A, B. And we're going to do that by drawing in a parallelogram. But first, let me style these objects so that I can draw some emphasis away from the circles. I'll choose the dotted line type.
And I'll just tap on each one of these circles so they're not so prominent. And then I'll turn off line type, and select black as the color and tap on the diagonal line. To make it a little bit bolder. I'll draw a parallel line and place that at B. I'll also make that black. Then I'll draw a line connecting G and B. That's one side of my parallelogram.
Need a corresponding line at a, I could draw a parallel or I can use this tool to transpose a distance. I'll drag from G to B. And then from a and I can see right here that it connects. And just to prove to you that this is a parallelogram, I'm going to label this as H. And then measure it. Let's say the distance from A to G should equal a distance from A to B. And it does and then a h should equal g h GB and it does.
Okay, so we have essentially a parallelogram here. Because of that, we should be able to copy the circles on the upper edge down to the lower edge. So I'm going to use this tool and measure from A to C and then position H and place that right there. Now I can draw circles as I did before. And you don't actually need a circle at B because we have all the information we need. Now I'll draw lines.
Well, first I'll label these. And then I'll draw lines connecting these dots. And it's where those lines cross the original segment AB, that we have our needed divisions. So I'm going to label these points. So let's verify that we've divided that red line into five equal parts. I'll measure the distance from A to M, that should be the same as m n. And it is and then m n should equal n o n n o should equal Op Op should equal PB.
So that's proof that we've divided it correctly.