Drawing parallel lines

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Here we construct a parallel through a given point using the compass and straightedge and also with the digital tool.

Transcript

In this video, we're going to draw a parallel line through the point A. I'll begin by making a point on the red line at some arbitrary location. And I'll label that B and then draw a circle from A to B, and another one from BDA. This creates another point over here on the right, which I'll label C, create another circle from C to A. And this creates a vesicle Pisco shape, which you could instantly use to bisect segment BC, if desired. That's not my goal. So I'll just continue on.

I'll place another point over here and label that D. I'll draw another circle from D to see so now we have three circles along the line with all the same size I'll locate a point right here. And then draw a line connecting point A to this new point E. It turns out that this line is parallel to the original line. I'll just make that red. And then to prove that it's parallel, I'll have to draw in a diagonal line somewhere. I can draw that between A and B, or between EMC, it doesn't really matter. I'll choose it over here.

And then just for sake of clarity, I'll create some points on that line, and another one right here. And then I'll label these points and then measure angles. So I'm going to measure this angle from A to E, and then E to F That sets up angle A E, F. And then I'll measure the similar angle down below G to C, and then C to E. And because these two similar length angles are equal, that proves that these lines are indeed parallel. If I want to create a parallel line using this specialized parallel tool, it's very easy. All you have to do is drag the pointer from an existing line and place it anywhere you want. So if I had a point, let's say right here, I could then label that and then I can make a parallel line that connects to that point.

So it's very easy to do using the parallel line tool. But now you know how to construct parallels using the digital tool, as well as the traditional method.

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