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  • - [Instructor] We have four triangles depicted here,

  • and they've told us that the triangles

  • are not drawn to scale.

  • And we are asked which two triangles must be congruent?

  • So pause this video, and see if you can work this out

  • on your own before we work through this together.

  • All right, now let's work through this together.

  • And it looks like for every one of these

  • or actually almost every one of these,

  • they've given us two angles,

  • and they've given us a side.

  • This triangle IJH, they've only given us two angles.

  • So what I'd like to do is,

  • if I know two angles of a triangle,

  • I can figure out the third angle because the sum

  • of the angles of a triangle have to add up to 180 degrees.

  • And then I can use that information,

  • maybe with the sides that they give us,

  • in order to judge which of these triangles are congruent.

  • So first of all, what is going to be the measure

  • of this angle right over here,

  • the measure of angle ACB?

  • Pause the video, and try to think about that.

  • Well, one way to think about it,

  • if we call the measure of that angle x,

  • we know that x plus 36

  • plus 82 needs to be equal to 180.

  • I'm just giving their measures in degrees here.

  • And so you could say x plus,

  • let's see 36 plus 82 is 118.

  • Did I do that right?

  • Six plus two is eight,

  • and then three plus eight is 11.

  • Yep, that's right.

  • So that's going to be equal to 180.

  • And then if I subtract 118 from both sides,

  • I'm going to get x is equal to,

  • 180 minus 18 is 62.

  • So this is x is equal to 62,

  • or this is a 62-degree angle,

  • I guess is another way of thinking about it.

  • I could put everything in terms of degrees if you like.

  • All right, now let's do the same thing

  • with this one right over here.

  • Well, this one has an 82-degree angle and a 62-degree angle,

  • just like this triangle over here.

  • So we know that the third angle needs to be 36 degrees,

  • 36 degrees.

  • Because we know 82 and 62,

  • if you need to get to 180, it has to be 36.

  • We just figured that out from this first triangle over here.

  • Now, if we look over here, 36 degrees and 59,

  • this definitely looks like it has different angles,

  • but let's figure out what this angle would have to be.

  • So if we call that y degrees,

  • we know, I'll do it over here,

  • y plus 36 plus 59

  • is equal to 180.

  • And I'm just thinking in terms of degrees here.

  • So y plus,

  • this is going to be equal to, what is this?

  • This is going to be equal to 95,

  • is equal to 180.

  • Did I do that right?

  • Yep, that's 80 plus 15, yep, 95.

  • And then if I subtract 95 from both sides,

  • what am I left with?

  • I'm left with y is equal to 85 degrees.

  • And so this is going to be equal to 85 degrees.

  • And then this last triangle right over here,

  • I have an angle that has a measure of 36,

  • another one that's 59.

  • So by the same logic,

  • this one over here has to be 85 degrees.

  • So let's ask ourselves, now that we've figured out

  • a little bit more about these triangles,

  • which of these two must be congruent?

  • So you might be tempted

  • to look at these bottom two triangles and say,

  • hey, look all of their angles are the same.

  • You have angle, angle, angle and angle, angle, angle.

  • Well, they would be similar.

  • If you have three angles that are the same,

  • you definitely have similar triangles.

  • But we don't have any length information for triangle IJH.

  • You need to know at least one of the lengths

  • of one of the sides in order to even think,

  • start to think about congruence.

  • And so we can't make any conclusion that IJH and LMK,

  • triangles IJH and triangles LMK are congruent to each other.

  • Now let's look at these candidates up here.

  • We know that their angles are all the same,

  • and so we could apply angle,

  • I'll do this in a different color,

  • angle, side, angle,

  • 36 degrees, length six, 82 degrees,

  • 36 degrees, length six,

  • 82 degrees.

  • So by angle, side, angle,

  • we know that triangle ABC

  • is indeed congruent to triangle DEF.

  • And we're done.

- [Instructor] We have four triangles depicted here,

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確定全等三角形的例子 (Determining congruent triangles example)

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    林宜悉 發佈於 2021 年 01 月 14 日
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