 Here's a quick example dealing with triangle with congruent legs. In other words, so we know for sure that this triangle is an isosceles Then it says classify the triangle by its sides Well, we know right off the bat that it's isosceles, but there might be something else going on So let's draw out a picture. We have triangle L M N and we know L M and M N are congruent. So let's say L M N And I know that L M is congruent to M M furthermore, we also know that the side lengths L M is 2x plus 6 M N is 12 and L N is 4x and Using the fact that these legs are congruent. I know that 2x plus 6 must equal 12 And so then we can solve that Figure out what x is So we get x is equal to 3 Which means if I plug in 3, let's say if I plug in 3 for this value of x Then we get 2 times 3 plus 6 Which is 12 And that was expected because this length and that length were shown to be equal However, if we plug in 3 for this length, then we have 4 times 3, which is also 12 And so when we go to classify this triangle by its sides and its angles We see not only is this an isosceles triangle It's actually equilateral and as we saw in the previous video if we have an equilateral triangle We also have an equi-angular triangle. If I give you triangle rstv Sorry rst and then I give you a couple of coordinates What are you going to need to do in order to classify by its sides? Well, you're going to need to graph it and Then you're going to need to use the distance formula to figure out how long those sides are So the distance formula says that rs is about 8.6 st is about 6.4 and Rt is about 9.2. So what that tells me is triangle rst If I am to classify by its sides It can either be scalene isosceles or equilateral since all the sides are different. This is indeed a scalene triangle