Write and evaluate the converse, inverse, and contrapositive of a conditional statement, and distinguish inductive from deductive reasoning.
A conditional statement has the form "if p, then q," where p is the hypothesis and q is the conclusion -- almost every theorem in geometry is secretly a conditional. From one conditional we can build three related statements: the converse swaps the hypothesis and conclusion ("if q, then p"), the inverse negates both ("if not p, then not q"), and the contrapositive negates AND swaps them ("if not q, then not p"). A conditional and its contrapositive always share the same truth value; the converse and inverse also match each other, but neither is guaranteed to match the original.
Inductive reasoning finds a pattern from several examples and guesses a general rule -- useful for forming a conjecture, but never a proof, since the very next example could break the pattern. Deductive reasoning instead starts from accepted facts (definitions, postulates, already-proven theorems) and uses logical steps to reach a conclusion that is guaranteed true. Geometry uses inductive reasoning to DISCOVER what might be true and deductive reasoning to PROVE that it actually is.
Mastery looks like: They correctly form the converse, inverse, and contrapositive of a conditional and can explain, with an example, why inductive reasoning does not count as proof.
Common stumbles: Confusing the converse with the contrapositive; assuming a conditional statement and its converse must have the same truth value.