## Video transcript

What we have drawn over hereis five different triangles. And what I want todo in this video is figure out whichof these triangles are congruent to whichother of these triangles. And to figure thatout, I'm just over here going to write our trianglecongruency postulate. So we know thattwo triangles are congruent if all of theirsides are the same-- so side, side, side. We also know they are congruentif we have a side and then an angle between the sidesand then another side that is congruent-- soside, angle, side. If we reverse theangles and the sides, we know that's also acongruence postulate. So if we have an angleand then another angle and then the side inbetween them is congruent, then we also have twocongruent triangles. And then finally, if wehave an angle and then another angle andthen a side, then that is also-- any of theseimply congruency. So let's see ourcongruent triangles. So let's see what we canfigure out right over here for these triangles. So right in thistriangle ABC over here, we're given this length 7,then 60 degrees, and then 40 degrees. Or another way tothink about it, we're given an angle, an angleand a side-- 40 degrees, then 60 degrees, then 7. And in order for somethingto be congruent here, they would have to have anangle, angle, side given-- at least, unless maybewe have to figure it out some other way. But I'm guessingfor this problem, they'll just alreadygive us the angle. So they'll have to have anangle, an angle, and side. And it can't just be anyangle, angle, and side. It has to be 40, 60, and 7, andit has to be in the same order. It can't be 60 andthen 40 and then 7. If the 40-degree sidehas-- if one of its sides has the length 7, then thatis not the same thing here. Here, the 60-degreeside has length 7. So let's see if any ofthese other triangles have this kind of 40,60 degrees, and then the 7 right over here. So this has the 40 degreesand the 60 degrees, but the 7 is in between them. So this looks likeit might be congruent to some other triangle,maybe closer to something like angle, side,angle because they have an angle, side, angle. So it wouldn't be that one. This one looks interesting. This is also angle, side, angle. So maybe these are congruent,but we'll check back on that. We're still focused onthis one right over here. And this one, we have a 60degrees, then a 40 degrees, and a 7. This is tempting. We have an angle, anangle, and a side, but the angles arein a different order. Here it's 40, 60, 7. Here it's 60, 40, 7. So it's an angle,an angle, and side, but the side is not onthe 60-degree angle. It's on the 40-degreeangle over here. So this doesn'tlook right either. Here we have 40 degrees,60 degrees, and then 7. So this is looking pretty good. We have this sideright over here is congruent to thisside right over here. Then you have your 60-degreeangle right over here. It might not be obvious,because it's flipped, and they're drawn alittle bit different. But you should never assumethat just the drawing tells you what's going on. And then finally, you haveyour 40-degree angle here, which is your40-degree angle here. So we can say-- we canwrite down-- and let me think of a goodplace to do it. I'll write it right over here. We can write down that triangleABC is congruent to triangle-- and now we have to be verycareful with how we name this. We have to makesure that we have the correspondingvertices map up together. So for example, we startedthis triangle at vertex A. So point A rightover here, that's where we have the60-degree angle. That's the vertex ofthe 60-degree angle. So the vertex of the 60-degreeangle over here is point N. So I'm going to go to N. And then we went from A to B. Bwas the vertex that we did not have any angle for. And we could figure it out. If these two guys addup to 100, then this is going to be the80-degree angle. So over here, the80-degree angle is going to be M, the one thatwe don't have any label for. It's kind of theother side-- it's the thing that shares the 7length side right over here. So then we want to go toN, then M-- sorry, NM-- and then finish upthe triangle in O. And I want toreally stress this, that we have to make sure weget the order of these right because then we're referringto-- we're not showing the correspondingvertices in each triangle. Now we see vertexA, or point A, maps to point N on thiscongruent triangle. Vertex B maps topoint M. And so you can say, look, the lengthof AB is congruent to NM. So it all matches up. And we can saythat these two are congruent by angle,angle, side, by AAS. So we did this one, thisone right over here, is congruent to thisone right over there. And now let's look atthese two characters. So here we have an angle, 40degrees, a side in between, and then another angle. So it looks like ASA isgoing to be involved. We look at this oneright over here. We have 40 degrees, 40degrees, 7, and then 60. You might say, wait, here arethe 40 degrees on the bottom. Then here it's on the top. But remember, thingscan be congruent if you can flip them-- ifyou could flip them, rotate them, shift them, whatever. So if you flipthis guy over, you will get this one over here. And that would nothave happened if you had flipped this one toget this one over here. So you see these two by--let me just make it clear-- you have this 60-degree angleis congruent to this 60-degree angle. You have this sideof length 7 is congruent to thisside of length 7. And then you havethe 40-degree angle is congruent to this40-degree angle. So once again,these two characters are congruent to each other. And we can write-- I'llwrite it right over here-- we can say triangle DEF iscongruent to triangle-- and here we have tobe careful again. D, point D, is the vertexfor the 60-degree side. So I'm going to start at H,which is the vertex of the 60-- degree side over here-- iscongruent to triangle H. And then we wentfrom D to E. E is the vertex on the 40-degreeside, the other vertex that shares the 7 lengthsegment right over here. So we want to gofrom H to G, HGI, and we know that fromangle, side, angle. And so that gives us thatthat character right over there is congruent to thischaracter right over here. And then finally, we're leftwith this poor, poor chap. And it looks like it is notcongruent to any of them. It is tempting to try tomatch it up to this one, especially because theangles here are on the bottom and you have the 7 sideover here-- angles here on the bottom andthe 7 side over here. But it doesn't match up,because the order of the angles aren't the same. You don't have the samecorresponding angles. If you try to do thislittle exercise where you map everythingto each other, you wouldn't be able todo it right over here. And this over here-- it mighthave been a trick question where maybe if youdid the math-- if this was like a 40 or a60-degree angle, then maybe you couldhave matched this to some of the other trianglesor maybe even some of them to each other. But this last angle, in allof these cases-- 40 plus 60 is 100. This is going to be an80-degree angle right over. They have to add up to 180. This is an 80-degree angle. If this ended up, by the math,being a 40 or 60-degree angle, then it could have been alittle bit more interesting. There might have beenother congruent pairs. But this is an 80-degreeangle in every case. The other angle is 80 degrees. So this is just a lone--unfortunately for him, he is not able to finda congruent companion.