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  • - [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.

  • I'm already, I'll already rule out C,

  • 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


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B1 中級

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