I am recently solving Problems & Solutions in Euclidean Geometry. I have learnt a lot of facts regarding to parallelogram, triangles, areas etc etc and solve quite a lot of questions. For the most part of questions, I can see through it either immediately or drawing all given information in detail. At any rate, the theorems can help me solve the problems.
But recently, I have come across some questions that after applying all theorems at first glance, I go nowhere. I have been sitting there for 5 hours per question. And right after I give up and look for the answer, all of my prior observations based on what I learnt from the theorems aren't even brought up in the solution!
For example,
The question asked me to prove $\Delta$ABC = $\Delta$ACE + $\frac{1}{2}\Delta$ABC
I didn't realize $\Delta$EAB$\cong \Delta$CAD when I was given $\Delta$ACE and $\Delta$ABD are equilateral. Then I wasted like an hour by struggling whether $\Delta$ACE $\cong\Delta$ACF. Turns out it simply isn't.
Another example, when only given G and H the mid-point and asked to prove Area $\Delta$EHG = $\frac{ABCD}{4}$. I can only observe 4ABHG = ABCD and achieve nothing for 3 hours again. Then when I read the solution, I understand it but I just can't come up with the theorems I learnt. It manipulated $\Delta$ABE, $\Delta$BGE and $\Delta$AHE, which are things that I have never thought of.
So my question is, how to train myself seeing through questions with several layer of abstractions, which obviously cannot be inferred by simply knowing the facts? To some extent, it seem beyond using the fact I have learnt in this book.
I have seen answer referring to more practices. But the problem more practices mean more frustration. I just can't see what I can't see.
My answer would be still "more practice". With more examples previously analyzed, your intuition is likely to improve, so you know what makes sense to look for. But don't burn out on problems where you've spent too much time already. After a reasonable attempt, find a solution from some source, analyze it, and go on to the next problem.
It's worth noting that complicated plane geometry problems relate very little to most parts of advanced math, so if you have goals beyond plane geometry, don't worry too much about it.