Unit 1 · Core unit
What counts as an argument. Geometry is the course where students first have to justify rather than compute, and this unit sets that expectation.
What a strong answer looks like
A strong answer pairs every statement with the definition, postulate, or theorem that licenses it.
Know
A conditional and its contrapositive are logically equivalent; its converse and inverse are not. Confusing them is the most common reasoning error in the unit.
Apply
Write all four forms and test each against an example.
Watch out
Assuming the converse follows from a true conditional.
Study move
Write the converse, inverse, and contrapositive of one statement and judge each.
Know
Inductive reasoning generalises from examples and can be wrong. Deductive reasoning derives a conclusion that must follow.
Apply
Use examples to form a conjecture, then prove it deductively.
Watch out
Treating a pattern confirmed on several cases as proved.
Study move
Form a conjecture from three cases, then find a counterexample or prove it.
Know
A proof is a chain of statements each justified by a definition, postulate, or previously proved theorem.
Apply
Write the given and the goal first, then work toward the goal one justified step at a time.
Watch out
Citing the diagram as a reason, when a diagram illustrates rather than justifies.
Study move
Prove a simple angle relationship in two-column form.
Modeling drill
Prove that vertical angles are congruent, citing a reason for every statement.
