I have concerns about the solution. Posted in comments.
First, is ADB not the ‘smaller-looking’ triangle instead?
Also, the relationship I see between AD/AB = AB/ BC is (side attached to the 90-degree angle) / hypotenuse. So, I am thinking the ratio for triangle CDB should be DC/ BC instead.
Yes, fixed.
What is the relevance of CDB?
It is not. I just wanted to know if I set it up right.
Put it this way: with two pairs of similar triangles, the relevant angles must match, and sides should be in proportion. So if you say that ABC and ADB are similar, it must be the case that AB/AD = BC/DB. Same with any other pair you may choose (such as CDB and CBA - CDB and ABC won’t work)
Unfortunately, I still don’t get it.
What exactly is that you don’t get?
I think I get it now. BDC is the triangle that shares an angle with ABC and not CDB, right?
Both triangles share an angle with ABC. The question is - which one? CDB and CBD may look like the same, but they aren’t when making similarity comparisons.
Alright. Thanks.