Proofs

Meet the two-column form where it is simplest — solving an equation. Every line is a statement paired with the reason that justifies it, and each step follows from the ones above.

Your first two-column proof — show that vertical angles are always equal by giving a reason for every step, building the argument one line at a time.

Prove length relationships on a line — when a point splits a segment, the two pieces add to the whole. Use the Segment Addition Postulate with substitution and the properties of equality to build the argument.

Prove angle relationships at a vertex — when a ray splits an angle, the two parts add to the whole. Use the Angle Addition Postulate with substitution and the properties of equality to build the argument.

The workhorse of geometry proofs — show two triangles are congruent by SSS, SAS, or ASA, then use CPCTC to conclude that a matching pair of sides or angles must be congruent too.

The capstone — proofs from every family, interleaved and unlabelled. You are not told which kind it is, so the first move is always the same — read the givens and choose the strategy.