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Current time:0:00Total duration:5:30

Classifying triangles by angles

CCSS.Math:

Video transcript

we've already seen that we can categorize triangles as being equilateral isosceles or scalene based on the lengths of the sides of the triangle so if none of the lengths are congruent so if you have something something like this we would consider this scalene I'm assuming that this side is not equal to that side and neither of these are equal to that side so that would be scaling and this is all a review if I have at least two of the sides being equal so say let's say that side is the same length as that side right over there we could call this so I'll mark it off as these are the same length this would be an isosceles I saw sceles triangle and then if all three of them all three sides are congruent so if all three sides are congruent if all three sides are the same length we would call this equilateral equilateral and in most circles you could also say this as isosceles because isosceles would be at least two sides being equal so this one definitely has at least two sides it has all three so this is you could say equilateral and isosceles while this one if we assume this third side is a different length this would just be isosceles not equilateral now all of that is review now what I want to think about in this video is what what if we're not given the lengths of the sides and what if we're just given a few of the angles so for example let's say we were given a triangle let's say that we were given a triangle where we're given where we're given a few of the angle measures so let's say we are told that this angle right over here is and let's say this angle right over here is 40 degrees and this angle right over here is 50 degrees now based on that could you somehow classify this as scalene isosceles or equilateral well the key here to realize is is if you know two angles two interior angles of a triangle you can always figure out the third because the three need to add up to 180 degrees so this is 40 that is 50 so these two add up to 90 so to add up to 180 degrees this one to be a 90-degree angle we can even mark it we can even mark it as a right angle and so if you have a triangle where all of the interior angles are different that means that all of the side lengths are going to be different and one way to think about is this if this angle became wider if this angle became wider this length let me actually show the corresponding so this angle is this if that angle right over there became wider then this length would have to become wider if this angle became larger or smaller then this side is going to have to become larger or smaller and if this angle became larger or smaller then this side is going to become larger and smaller so hopefully you see it appreciate that if you have three different angles you're going to have three different side lengths so just based on the angles here that we have three different angles we can say that this is going to be a scalene a scalene triangle now we can look at a couple other examples what if we knew what if we knew that what if we knew let's do an interesting one what if what if this angle actually let me let's say this angle is let's say this angle right over here is I don't know let's say it is 70 degrees and let's say this angle over here is 40 degrees now based on the information I've given you what kind of triangle is this going to be or can you even figure it out well we use the same idea the interior angles need to add up to 180 70 plus 40 is 110 so you could say 110 plus what is equal to 180 degrees well this is going to have to be 70 degrees so this angle right over here is 70 degrees and so now we have a scenario where two of the angles have the same measure and so this angle is really one way to think about it based on whether this angle is large or small it's going to define the length of that side and this angle right over here depending on how large or small it is is going to define the length on this side and so because these two angles are congruent because they have the same measure they're opposite sides are going to be congruent so this is going to be the same as that and so just based on the information I had started giving you if you if because you can show that two angles are going to be the same you can say that this is going to be an isosceles isosceles triangle and now let's do a third example and you could probably guess what I'm going to do in this third example if I can if I have let's say this angle is 60 degrees this angle is 60 degrees what type of a triangle is this going to be well if this is 60 this is 60 to make them add up to 180 this would have to be 60 that would have to be 60 degrees as well and if you have all of the angles are congruent that that means that all of the sides are congruent and so now you are dealing with an equilateral now as we said before this is also you could view this as a subset of isosceles because you have at least two angles and you have two sides being congruent but here it's all three so this is an equilateral triangle