First you need to explain what sort of theory or axioms underlie all this, because that determines what techniques can be used.
I can see how to do #1 directly, but the instruction "Prove indirectly" is quite puzzling. Also, ## 2, 3 and 4 need more information than the diagrams show. In #2 I guess AC is meant to be a diameter. In #3 you need some information about lengths or angles in those triangles. In #4 the rhombus has to be special in some way before you can prove it is a square. It would be best to post the _complete_ wording of the original questions, as the details do matter.