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Good day students in this clip we are going to be going over two examples on how to solve special triangles that are composite. so lets take a look at the first question.in number 1 it says a kite is made up of a pair of 30-60-90 and a pair of 45-45-90 triangles what is the length of the main diagonal. alright so what we are going to do is make a sketch of this situation and then label our cross and main diagonals and also the angles ok. so let us start off by drawing the kite. alright so there goes the kite so we know what a kite is it is basically a quadrilateral where two disjoint pairs of consecutive sides are congruent. So this is the first disjoint pair and these two sides are congruent lets go ahead and mark it so this side is congruent to that side. and this is the second disjoint pair of consecutive sides and these are also congruent to each other. they are disjoint because these two go together and these two go together and if you group them in another configuration you are not going to have congruent pairs. that is why there are disjoints. alright so what else can we tell from this triangle right here we know that this segment right here is the, this is the main diagonal.Ok this is the main diagonal.and this segment right here is your cross diagonal. we know that the main diagonal bisects the cross diagonal so we can also indicate that this segment right here is congruent to that segment so what do we know about the triagnles? we know that one pair is 30-60-90 and the other pair is 45-45-90 which do you think is the 30-60-90 pair and which do you think is the 45-45-90 pair? If you look at this triangle right here and this triangle right here it is easy to see that this is the 45-45-90 pair alright this here is 45 degrees and the angle right here is 45 and this is 90 degrees right here ok. this is a 45-45-90 triangle this side right here is going to be congruent to this side right here. this triangle right here is the 30-60-90 triangle. The question is which is the 30 and which is the 60 degrees? we can clearly see that this is the smaller of the two. so this angle right here is the 30 degrees angle and the angle right here is the 60 degree now we are told that the lenght of the cross diagonal is four root 2 so the length from here to here when projected out from here to here it is four root two. Okay so the entire thing is four root two if we split it down the center if we split it in half what is the measure of half of that be? if we split it down the center the distance from here this portion right here to this portion right here is going to be half of the entire length. What will that be? it is simply going to be four root 2 divided by 2. so what do you get when you divide the four root two by two? if you divide four root two by two, lets do that on the sided here four root two divided by two. Two goes here one two goes here two. so is is going to be two root two. Alright so the length of half of the cross diagonal is going to be two root two. Ok so how are we going to find the length of the main diagonal? we have to find this portion right here and we also have to find this portion right here. in order to do this it will be beneficial for us to split this problem into two triangles.
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