My question is raised from this problem:
It's known that the isosceles triangle $AB$ is similar to $CD$. Let's say the ratio of the area of those two triangle is $x\,:\,y$.
My question is, if I draw a cyan line so that I have a triangle $E$ (the big cyan triangle) so that it will similar to the small triangle $D$ (small cyan), will the ratio of $E$ and $D$ be $x\,:\,y$ as well? If yes, could you explain it briefly regarding the proof?
My original problem, I have to find the ratio of the triangle $A$ and $D$ which looks like they're similar as well. However, that's not what I'm going to ask here. The question has already written above. Mentioning my original problem, probably you could understand why I ask this.