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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,

B1 中級

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

• 2 0
林宜悉 發佈於 2021 年 01 月 14 日