I also have the same problems in proving maths questions.Then i practised hard that question.Watching their solutions and explanation. Understanding theorems , practising More books like R.D. Sharma etc .Now i have no problems in solving these types of questions.They become very simplier and easier for me. My friend , from my point of view you also have to start practising on these type of questions.
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Wat u could do is that practise using rd , rs and even the ncert is tough enough 
had that same problem some time ago , but now its all sorted out ..
1) you first gotta aim at wat u wanna prove
if you have angles in it , name them as angle 1, 2,3 ; trust me thats gonna help you 
TIP - never ever find logic in these questions cause there isn't 
2) then the second step would be using all the properties you know , e.g. angle sum property , exterior angle , wateva it is 
then form some equations using them
3) then either you have to equate them , add/subtract them or put the value of one equation into another. 
these are the three common methods of the "proving" questions 

follow these and its not gonna be a problem for u