Unit 3: Reasoning and Proof, Unit Review

Paragraph Proof

A paragraph proof is another way a proof is often written.

Biconditional

A single true statement that combines a true conditional and its true converse.

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.

Conditional

An if-then statement.

Contrapositive

If not q, then not p.

Equivalent Statements

Statements with the same truth value.

Inverse

The inverse of the conditional "if p, then q" is the conditional "if not p, then not q."

Negation

The negation of a statement has the opposite meaning of the original statement.

Hypothesis

The part p following if.

Conclusion

The part q following then.

Converse

The statement obtained by reversing the hypothesis and conclusion of a conditional.