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Stuff I need to study.

Inductive reasoning
Counterexamples
Geometric Induction
Deductive Reasoning
Conditional statements
The hypothesis and conclusion of a conditional statement
The converse of a conditional statement
Biconditional statements
The inverse of a conditional statement
The contrapositive of a conditional statement
Truth tables
The Law of Detachment
The Law of Syllogism
The properties of equality from Algebra
Hot the properties of equality apply to Geometry
Theorems, postulates, and definitions
Informal proofs
Two-column algebraic proofs
Two-column geometric proofs
Proofs by contradiction
 
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1 Answer

This sounds like the entirety of most textbooks' chapters on geometric proofs.  I assume you have a textbook for your math class, right?  I'd just find the chapter on proofs and read through it carefully - most of the terms you mentioned have simple one or two-sentence definitions which should be in your textbook.
 
If you need help understanding the terms themselves, I'm available for online geometry tutoring.  Check out my profile; I'd be happy to work with you a bit more in-depth and make sure you understand the concepts.