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  • - [Instructor] What we're gonna do in this video

  • is learn to construct congruent angles,

  • and we're gonna do it, with of course,

  • a pen or a pencil here.

  • I'm gonna use a ruler as a straight edge.

  • And then I'm gonna use a tool

  • known as a compass.

  • Which looks a little bit fancy,

  • but what it allows us to do

  • it'll apply using it in a little bit,

  • is it allows us to draw perfect circles,

  • or arcs, of a given radius.

  • You pivot on one point here

  • and then you use your pen or your pencil

  • to trace out the arc,

  • or the circle.

  • So let's just start with this angle

  • right over here,

  • and I'm going to construct an angle

  • that is congruent to it.

  • So let me make the vertex of my second angle

  • right over there,

  • and then let me draw one of the rays

  • that originates at that vertex.

  • And I'm gonna put this angle

  • in a different orientation,

  • just to show that they don't even have

  • to have the same orientation.

  • So it's going to look

  • something like that, that's one of the rays.

  • But then we have to figure out

  • where do we put,

  • where do we put the other ray

  • so that the two angles are congruent?

  • And this is where our compass

  • is going to be really useful.

  • So what I'm going to do is put the pivot point

  • of a compass, of the compass,

  • right at the vertex of the first angle,

  • and I'm going to draw out an arc like this.

  • And what's useful about the compass

  • is you can keep the radius constant,

  • and you can see it intersects

  • our first two rays at points,

  • let's just call this B and C.

  • And I could call this point A,

  • right over here.

  • And so let me,

  • now that I have my compass with the exact

  • right radius right now,

  • let me draw that right over here.

  • But this alone won't allow us to draw

  • the angle just yet,

  • but let me draw it like this,

  • and that is pretty good.

  • And let's call this point right over here D,

  • and I'll call this one E,

  • and I wanna figure out where to put

  • my third point F,

  • so I can define ray E F,

  • so that these two angles are congruent.

  • And what I can do is take my compass again

  • and get a clear sense of the distance

  • between C and B,

  • by adjusting my compass.

  • So one point is on C,

  • and my pencil is on B.

  • So I have, get this right,

  • so I have this distance right over here.

  • I know this distance,

  • and I've adjusted my compass accordingly,

  • so I can get that same distance

  • right over there.

  • And so you can now image

  • where I'm going to draw that second ray.

  • That second ray,

  • if I put point F right over here,

  • my second ray,

  • I can just draw between, starting at point E

  • right over here,

  • going through point F.

  • I could draw a little bit neater,

  • so it would look like that, my second ray.

  • Ignore that first little line I drew,

  • I'm using a pen,

  • which I don't recommend for you to do it.

  • I'm doing it so that you can see

  • it on this video.

  • Now how do we know that this angle

  • is now congruent to this angle

  • right over here?

  • Well one way to do it, is to think

  • about triangle B A C,

  • triangle B A C,

  • and triangle, let's just call it D F E.

  • So this triangle right over here.

  • When we drew that first arc,

  • we know that the distance between A C

  • is equivalent to the distance between A B,

  • and we kept the compass radius the same.

  • So we know that's also the distance between E F,

  • and the distance between E D.

  • And then the second time,

  • when we adjusted our compass radius,

  • we now know that the distance between B C

  • is the same as the distance between F and D.

  • Or the length of B C

  • is the same as the length of F D.

  • So it's very clear that we have congruent triangles.

  • All of the three sides

  • have the same measure,

  • and therefore the corresponding angles

  • must be congruent as well.

- [Instructor] What we're gonna do in this video

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B1 中級

幾何学的構造: 合同角度 (Geometric constructions: congruent angles)

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    林宜悉 に公開 2021 年 01 月 14 日
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