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  • - [Instructor] So I have two triangles depicted here

  • and we have some information about each of those triangles.

  • We know that this side of this left triangle

  • has length eight.

  • We know that this side has length seven

  • and then we know that this angle is 50 degrees.

  • And on this triangle we see some things that look

  • a little bit familiar.

  • This triangle, this side has length eight.

  • This side has length seven.

  • And this angle right over here has a measure of 50 degrees.

  • So my question to you is,

  • can you definitively say, not assuming

  • that these are drawn to scale,

  • because they actually aren't, can you definitively say

  • that these triangles are congruent?

  • Or could you definitively say that they aren't congruent?

  • Or can you not say either?

  • Would you have to say that there's not enough information?

  • Pause this video and think about that.

  • So essentially what we have here are two pairs of sides

  • that have the same length and and angle,

  • but that angle is not between those two sides.

  • If the angle were here and here,

  • then we could use side, angle, side, side, angle, side

  • to deduce that, hey, these are congruent,

  • but that's not what we're dealing with.

  • We are dealing with side, side, angle.

  • Side, side, angle.

  • I'm saying the side and the side before the angle,

  • because if I don't do that it becomes a little bit crass.

  • So what we're really saying

  • is side, side, angle sufficient to prove congruency?

  • And the reason why it's not,

  • is that you can actually construct different triangles

  • with the same constraints.

  • For example, on this right most triangle

  • it could look like this,

  • or it could look like this.

  • The seven side could go down like this

  • and intersect just like that.

  • Now you might be saying, hey, that's not what it looks like.

  • It looks very similar, but remember,

  • we're not going on looks.

  • We have to go based on the information they've given us

  • and so you could just as easily, based on the information,

  • the constraints they've given us,

  • have a triangle like this.

  • And so the very fact that you can create

  • two different triangles that are clearly not congruent,

  • based on the exact same information,

  • the exact same constraints, tells you that

  • that information, those constraints,

  • are not enough to tell you

  • that these are congruent triangles.

- [Instructor] So I have two triangles depicted here


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B1 中級

合同性に関する情報 (Information for congruency)

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    林宜悉 に公開 2021 年 01 月 14 日