I'm going to bisect a line in this video. And I'll start by using the traditional construction technique. And then later, I'll show you some quick ways of doing it in the app. Let's begin by drawing in a line segment of arbitrary length. Now I'd like to line this up with the screen. So I'll use the Hand tool, and then use two fingers on the screen to pan or zoom.

And also, if you rotate your two fingers relative to one another, you can rotate that on the screen. What I'm going to do is use the top edge of the screen as a guide to help me line this up and make it horizontal. And then I can bring that back in the center of the screen and maybe zoom out somewhat like that. Note that the bottom of the screen doesn't really work as a guide because it fades out down there. If you want to make a line vertical, you could use the left or the right edges of the screen Either way, it's fine. So this is simply analogous to drawing a line on a piece of paper and rotating the paper, just a good way to get started.

Now I'd like to label the endpoints of the line so that we have a common vocabulary. And you can do that by choosing one of the different tool sets at the bottom of the screen. Right now we're in the drawing tool set. There are different tool sets. Here's a decoration tool set the color and the label tool sets. I want to use the label tool set and its icon splitter a, and then letter alpha.

The Latin alphabet is useful for labeling points, and the Greek alphabet is more commonly used to label angles. So I'll stick with the Latin alphabet. And then I'll just click the left endpoint and the right endpoint to have it automatically label these with sequential letters in the alphabet. Incidentally, if you wanted to change the letter, you can just drag left and right on this control down here. Let's say I wanted that to be point G. I can then just tap on the right endpoint and it changes the label just like that. You can also have numerical subscripts if you'd like.

So let's say we wanted this to be g sub one, I could then tap on the item here on the right. And that opens up a different control with numbers in it. So now it's g one. If I tap on the right, it should say g one now. So this is a very flexible way of labeling things. I want that to say B though.

So I'm going to go back here, make that a dash, and tap on the left. Make this say B. And then if I tap on the endpoint on the right, change it back to letter B. So now we have line A, B, and my goal is to bisect that in the middle. I'll go to the drawing tool set here. And I'll draw in a circle from A to B, and then another circle from B to A.

This is called the vesica discus form, which means the vessel of the fish It's also known as a man door law or Almond. It's a very common form in sacred geometry. And it's the basis of many geometric constructions. Each one of the circles has its center point on the circumference of the opposite circle. So it's a symbol of duality of equality. And it's the, also known as the womb of creation where a lot of geometric forms spring forth out of this very simple and fundamental relationship.

In this video, we just want to bisect the line. And we can do that by drawing in a vertical. But first, we need to figure out where we're drawing that from. And those two circles intersect each other at the top and the bottom. And we need to identify those points first. There's a tool here on the right of the toolbar, which is intersection.

And I'll just tap on the top and the bottom of the vesica and that identifies those two points accurately. Now I'll go to the label tool and I'll just label that C and D by tapping on those two points again. And then I'll go back to my drawing tool set, draw a line from point C to D. and then put in an intersection point where the two lines cross. And then I'll label that as point E. Now I'd like to determine if a equals Eb, it looks like they do, but we can't really be sure, unless we check it out. And that's here under decorations. Now, there are different ways to decorate your drawing.

And you can do it by measuring lengths of lines, angles, angles and degrees, or right angles. I'm concerned with the length of lines. And the way that this works as you drag from point A to D. And then you drag from point A to B and it will only show up as a decoration. If in fact it is truly equal, and you can see that it is this can be toggled, off and on. And that's proof that we've bisected the line. So this is how you would do it traditionally, although you might not draw the whole circles, you might just draw little arc segments.

To locate points C and D, this would be the technique that you would use to bisect any line segment. If you're using the app, you don't need to go through all of these steps necessarily. For example, I'm going to zoom out and draw in a new line segment below have some arbitrary length. I'd like to label that points F and G. Now I'd like to bisect that. And there's a specialized tool for that purpose right here. And it works by dragging from point F to G. It puts in the bisection point right there.

So I'm going to label And then I'll verify that f h equals h, g. And it does. There's a similar tool adjacent, this puts in the perpendicular bisector. So I can drag from F to G. Not only does it bisect the line, but it also puts in the perpendicular. In this case, I don't really need that I'm going to undo by tapping the arrow in the lower right hand corner of the screen to go back a step. So now you see how you can bisect a line either either using the traditional method or using the specialized tools in the app.