Auxiliary Lines  -  Lines that are created to help prove a statement.

Contradiction  -  The situation that occurs when the negation of a true statement is also true. A contradiction signifies that there has been a mistake in reasoning, and can be used in building indirect proofs.

Direct Proof  -  A proof in which the conclusion is drawn directly from previous conclusions, starting with the first statement.

Geometric Proof  -  A step-by-step explanation that uses definitions, axioms, postulates, and previously proved theorems to draw a conclusion about a geometric statement. There are two major types of proofs: direct proofs and indirect proofs.

Indirect Proof  -  A proof in which a statement is shown to be true because the assumption that its negation is true leads to a contradiction.

Paragraph Proof  -  A kind of proof in which the steps are written out in complete sentences, in paragraph form. Identical in content, but different in form, from a two-column proof.

Two-Column Proof  -  A kind of proof in which the statements (conclusions) are listed in one column, and the reasons for each statement's truth are listed in another column. Identical in content, but different in form, from a paragraph proof.