What is the best strategy to take towards a Geometry-Related Proof?

Same with any proof. Look at the given parameters, and note what conclusions can immediately be taken from them.

Well, I am not sure exactly what you are asking, but in modern geometry one is often interested in how geometric objects on a manifold M (tensor fields, densities, connections etc.) transform, usually under the diffeomorphism group of M or a subgroup of it.

 

 

So, depending on exactly what you want to prove, being very clear on what type of objects you have to deal with (identified by how they transform) is important.

Well, by looking at the nature of Asians other threads, it seems he meant Basic Deductive Geometry, such as showing 2 triangles are similar etc.

 

Look at what information you have. What can be deducted from those. Sum it all together, make a conclusion. Exactly what the tree said.