High school geometry
- Triangle congruence postulates/criteria
- Determining congruent triangles
- Calculating angle measures to verify congruence
- Determine congruent triangles
- Corresponding parts of congruent triangles are congruent
- Proving triangle congruence
- Prove triangle congruence
- Triangle congruence review
Calculating angle measures to verify congruence
Calculate missing angle measures to determine which triangles must be congruent. Created by Sal Khan.
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- Can someone please tell me an overview of this?? I am kinda confused. Thanks!(2 votes)
- Every triangle must add up to 180. If I have 2 angles that are 35 degrees each, I get 70 degrees total. When I subtract 70 from 180 I am left with 110 degrees which is the measure of the 3rd angle. Hope this helped!(4 votes)
- We know by ASA that they are congruent but can't we also use ASS to see that they are congruent? Or is there only one option?(2 votes)
- how can you tell which two triangles are congruent if they all look the same(1 vote)
- Why does Sal always start his explanation with "one way to think about it"? Don't get me wrong, I think it's a very good way to start a explanation, as it doesn't set up his explanation as the only valid piece of reasoning, but I'm just curious.(1 vote)
- That would be because his view is not the only valid one, just the one he chooses to teach here. I like that he acknowledges the reality that there are other methods used to solve these problems. Some users come from educational backgrounds that use different systems, like sometimes Sal teaches both methods and then asks which one your class uses.(1 vote)
- 1:21he said he was going to subtract 118 from both sides then only subtracted 18 from 180 why didn't he substract 118(0 votes)
- He subtracted 118 but accidently said 18. 180 - 118 is 62 (this is what sal got) so we know this is true(3 votes)
- [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 equals 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. Yeah, that's right. So that's going to equal to 180. And then if I subtract 118 from both sides, I'm going to get x is equal to 180 minus 118 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? Yeah, 80 plus 15, yeah, 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 measured 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 start to think about congruence. And so we can't make any conclusion that IJH and LMK, triangles IJL 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 FDE.