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CCSS.Math:

what I want to do in this video is talk about the two main ways that triangles are categorized the first way is based on whether or not the triangle has equal sides or at least a few equal sides and the other way is based on the measure of the angles of the triangle so the first categorization right here and all of these are based on whether or not the triangle has equal sides is scalene and a scalene triangle is a triangle where none of the sides are equal so for example if I have a triangle like this where this side has length 3 this side has length has length 4 and this side has length 5 and this size side has length 5 then this is going to be a scalene triangle none of the sides have an equal length now two isosceles triangle is a triangle where at least two of the sides have equal lengths so for example this this would be an isosceles triangle maybe this has length this has length 3 this has length 3 and this has length 2 notice this side and this side are equal so it meets the constraint of at least two of the three sides are have the same length now an equilateral triangle you might imagine it and you'd be right is a triangle where all three sides have the same length so for example this would be an equilateral triangle and let's say that this has side two two and two or if I have a triangle like this where it's three three and three any triangle where all three sides have the same length is going to be equal a Turrell now you might say well Sal didn't you just say that isosceles triangle is a triangle that has at least two sides being equal wouldn't an equilateral triangle be a special case of an isosceles triangle and I would say yes you are absolutely right an equilateral triangle has all three sides equal so it meets the constraints for an isosceles so by that definition all equilateral triangles are also isosceles triangles but not all isosceles triangles are equal at all so for example this one right over here this isosceles triangle clearly not equilateral and all three sides are not the same only two are but both of these equilateral triangles meet the constraint that at least two of the sides are equal now down here we're going to classify based on angles an acute triangle is a triangle where all of the angles are less than 90 degrees so for example so for example a triangle like let me a triangle like this maybe this is 60 let me draw a little bit bigger so I can draw the angle measures so triangle a triangle and that it's a little bit less I want to make it a little bit more obvious so let's say a triangle like this if this angle is 60 degrees maybe this one right over here is 59 degrees and then this angle right over here is 61 degrees notice they all add up to 180 degrees this would be an acute triangle notice all of the angles are less than 90 degrees so less than 90 degree angles for all of them a right triangle is a triangle that has one angle that is exactly 90 degrees so for example this this would be this right over here would be a right triangle maybe this angle or this angle is one it's 90 degrees a normal way that this is specified people wouldn't just do the traditional angle measure and write 90 degrees here they would normally write do this little they would draw the angle like this they would put a little I guess you could the edge of a box looking thing and that tells you that this angle right over here is 90 degrees and because this triangle has a 90 degree angle it can only have one 90 degree angle this is a right triangle so that is equal to 90 degrees now you could imagine an obtuse triangle based on the idea that an obtuse angle is larger than 90 an obtuse triangle is a triangle that has one angle that is larger than 90 degrees so let's say that you have a triangle that looks like this a triangle that looks something something like this maybe this is 120 degrees and then let's see let me make make sure that this would make sense maybe this is 25 degrees and maybe this is 34 maybe that is 35 degrees this is 25 degrees notice they still add up to 180 or at least they should 25 plus 35 is 60 plus 120 is 180 degrees but the important point here is that we have an angle that is larger that is greater greater than 90 degrees now you might be asking yourself hey Sal can kind of triangle be multiple of these things can it be a right scalene triangle absolutely you could have a right scalene triangle in this situation right over here actually a 3 4 5 triangle triangle has lengths of 3 4 & 5 actually is a right triangle this right over here would be a 90 degree angle you could have an equilateral acute angle acute triangle in fact by both all equilateral triangles because all of the angles are exactly 60 degrees all equilateral triangles are actually acute so there's multiple combinations that you can have between these situations and these situations right over here