all right now ladies and gentlemen when we're looking at this one thing i might uh recommend to you guys all right to do this is rather than having these triangles right on top of each other what i would do is i would recommend breaking these triangles up so they kind of make a little bit more sense as far as what you're looking at as far as what angles are related to what angles all right so rather than containing them all in one figure a lot of times you guys can just break them up and just redraw them and what that does is that allows us to kind of see what angles are congruent to what angles all right now i'm going to do this in two different ways you can write it as angle j is congruent to angle h we know that because they both have their um h's right you know we both have their 90 degree angles but also looking at your congruency statement we can see that these these side lengths all right since these are also equal to each other all right what we can determine jared is that angle k is not congruent to the other angle k these two angles are not equivalent all right it doesn't break it up evenly but we can say that k is congruent to our angle g so i can say angle k is congruent to angle g then you can look over here and you could say that well if this angle k is equal to angle g then this angle g is equal to that angle k and you might think of this as like all right well this is kind of getting a little bit confusing because we both have k's and g's for both triangles so a way we can get around that is we can rewrite the angles we can rewrite i'm sorry the angles using different notation how else can we write an angle besides just what the what the vertex is we can also label it using a prime we could use prime yeah i mean you could relabel this but um you could relabel this and say that's g prime and that's k prime that would work you know as well we could also use three points so therefore that would be j k prime and g prime you could also use three points to represent this angle g you could say angle j g k is congruent to angle h hey jared i asked you not right now is actually also and congruent to angle h kg so rather than just always using points remember we can also go back and use three um three points to represent the angle all right um so you could do that for the other one as well if you didn't if you wanted to use the prime so it's j g prime k prime or j j g k is congruent to h k g if you got away from the primes all right so that's another way and so then the other one would been angle j kg is congruent to angle h g k all right and the last one we just need to go for the side lengths so if these two are equal then we could say that these two are are equal because we know they're the same side and then we can prove that we could show that these two are going to be current so we could say that side j j g is congruent to h k you could say that g k is go ahead and congruent to k kg and then the last one we could do is jk is going to be congruent to hg okay so there's a couple different ways you guys could do the angles for this one um to make it not as much confusing and then you can go and determine your sides so therefore now we can determine these triangles is triangle g j k is congruent to triangle k h g all right please be careful with that because i know a lot of students what they'll do is they'll say triangle gj gjk is congruent to triangle g h k but g is not congruent to that g right these two angles are not corresponding right these are not corresponding angles these two angles are corresponding and these two angles are corresponding okay so just be careful with that all right