How do I know which sides of a triangle are proportional in similar triangles?

Question

Please refer to this link for the diagram.

So I know $\triangle ACE$ is similar to $\triangle BCD$. This is because $\angle BDC=\angle CAE=90^\circ$ and $\angle BCD$ is common to both triangles.

However, how do I know which sides are proportional to each other just by looking?

I am a bit confused here. Is $CD$ proportional to $AE$ or $BD$ proportional to $AE$? The only thing I can deduce is $BC$ is proportional to $EC$ since they are the hypotenuse. So, I get the following:

$\frac{BD}{AE}=\frac{CD}{AC}=\frac{BC}{EC}$ or $\frac{BD}{AC}=\frac{CD}{AE}=\frac{BC}{EC}$

Which one's correct and how can I prove that? Also, how can you tell which sides are proportional to each other in more complex triangles if you know they are similar?

Answer 1

Yes you should know which sides are proportional to each other just by looking, because the propotional sides are the opposites at the same corner. So in this case, $\frac{BD}{AE}=\frac{CD}{CA}=\frac{CB}{CE}$.

this could be usefull for you.

Answer 2

It's all about angles. $\angle CBD=180°-90°-\angle ACE=\angle AEC$ so $CD$ is proportional to $AC$.