Main content
High school geometry
Course: High school geometry > Unit 3
Lesson 3: Congruent triangles- 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
© 2023 Khan AcademyTerms of usePrivacy PolicyCookie Notice
Calculating angle measures to verify congruence
Calculate missing angle measures to determine which triangles must be congruent. Created by Sal Khan.
Want to join the conversation?
Can someone please tell me an overview of this?? I am kinda confused. Thanks!(3 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!(5 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?(3 votes)
First off: I wouldn't suggest using that term, you may get flagged/get some rude comments. Use SSA instead.
Next: Check out a few of the previous videos, Sal goes over this to prove why SSA doesn't work. And for your last comment... ASA is not the only postulate. The triangle congruency postulates (as covered so far) are: SAS, ASA, AAS, and SSS.(1 vote)
- how can you tell which two triangles are congruent if they all look the same(2 votes)
It is the angle numbers. With knowing all of the angles it is much easier figuring out which two triangles are congruent. And remember the size also has to be the same. Otherwise there is not much information to support the congruence of the triangles(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.(2 votes)
In order to figure out if an angle is congruent or not, use your congruent angle postulates: A-S-A, A-A-S, S-A-S, or S-S-S. Keep in mind that even if your angle sides are the same, this does not mean your angles are congruent. This does mean that they are similar, though.(1 vote)
It is confusing because you appear to be talking about triangle congruence, you cannot have "an angle is congruent" since congruency has to do with pairs of angles or two figures. Also, the postulates/theorems are for congruent triangles, not congruent angles. As you noted, SSS is one of the triangle congruence theorems, so if the three sides are the same, then the two triangles are congruent and thus the angles are also congruent.(2 votes)
Couldn't we use AAS instead of ASA?(1 vote)- Yes that would be fine. In fact, that uses what is originally given instead of something Sal calculated.(1 vote)
am I able to write the name of the triangle in any arrangmnent I want or is it specific(1 vote)
It is specific. For example Triangle ABC ≅ Triangle DEF, it means angle A = angle D, angle B = angle E, angle C = angle F. And side AB = DE etc.(1 vote)
- at4:20, Sal says to use ASA for triangles ABC and DFE to prove congruency. Could he also have used AAS, with 62 and 82 degrees, then a line of 6?(1 vote)
- Yes, you can. But now you have to write CBA ≅ EDF.
Also please check other comments before asking to avoid making duplicate questions.(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)
4:20Video transcript
- [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.