## 字幕列表 影片播放

• - [Instructor] We are told that Shui concluded

• the quadrilaterals, these two over here,

• have four pairs of congruent corresponding angles.

• We can see these right over there.

• And so, based on that she concludes

• that the figures are similar.

• What error if any, did Shui make in her conclusion?

• Pause this video and try to figure this out on your own.

• All right, so let's just remind ourselves

• one definition of similarity

• that we often use on geometry class,

• and that's two figures are similar

• is if you can through a series of

• rigid transformations and dilations,

• if you can map one figure onto the other.

• Now, when I look at these two figures,

• you could try to do something.

• You could say okay, let me shift it

• so that K gets mapped onto H.

• And if you did that,

• it looks like L would get mapped onto G.

• But these sides KN and LM right over here,

• they seem a good bit longer.

• So, and then if you try to dilate it down

• so that the length of KN is the same as the length of HI

• well then the lengths of KL and GH would be different.

• So it doesn't seem like you could do this.

• So it is strange that Shui concluded that they are similar.

• So let's find the mistake.

• that it's a correct conclusion

• 'cause I don't think they are similar.

• So let's see.

• Is the error that a rigid transformation, a translation

• would map HG onto KL?

• Yep, we just talked about that.

• HG can be mapped onto KL

• so the quadrilaterals are congruent, not similar.

• Oh, choice A is making an even stronger statement

• because anything that is congruent is going to be similar.

• You actually can't have something that's congruent

• and not similar.

• And so, choice A does not make any sense.

• So our deductive reasoning tells us it's probably choice B.

• But let's just read it.

• It's impossible to map quadrilateral GHIJ

• onto quadrilateral LKNM using only

• rigid transformations and dilations

• so the figures are not similar.

• Yeah, that's right.

• You could try, you could map HG onto KL,

• but then segment IJ would look something like this,

• IJ would go right over here.

• And then, if you tried to dilate it,

• so that the length of HI and GJ matched KN or LM,

• then you're gonna make HG bigger as well.

• So, you're never gonna be able to map them onto each other

• even if you can use dilations.

• So I like choice B.

- [Instructor] We are told that Shui concluded

B1 中級

# 類似的形狀和變換 (Similar shapes & transformations)

• 0 0
林宜悉 發佈於 2021 年 01 月 14 日