Logic, Relationships, and Theorems
This domain tests whether you can reason from given information rather than from a picture. You must know the building blocks: conditional statements (if p, then q), the converse (if q, then p), the inverse (if not p, then not q), and the contrapositive (if not q, then not p). Only the contrapositive is logically equivalent to the original; the converse and inverse are equivalent to each other but not to the original. Know the difference between inductive reasoning (patterns to a conjecture) and deductive reasoning (general rules to a specific conclusion), and be able to identify a counterexample that kills a conjecture.
You also need the standard theorem toolkit: vertical angles are congruent, linear pairs are supplementary, complements and supplements of the same angle are congruent, and parallel lines cut by a transversal produce congruent alternate interior, alternate exterior, and corresponding angles, with same-side interior angles supplementary. Traps: assuming a figure is drawn to scale, assuming the converse of a true statement is true, and confusing "same-side interior" (supplementary) with "alternate interior" (congruent). Another trap is the difference between a definition, a postulate, and a theorem when a question asks what justifies a step.
Worked example. Given: angle 1 and angle 2 are supplementary; angle 2 and angle 3 are supplementary. Prove angle 1 is congruent to angle 3. By the definition of supplementary, m1 + m2 = 180 and m2 + m3 = 180. Set them equal: m1 + m2 = m2 + m3. Subtract m2 from both sides: m1 = m3, so the angles are congruent. This is the Congruent Supplements Theorem, and the justification chain (definition, substitution, subtraction property) is exactly what multi-step proof questions reward.