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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

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