MATH 01310 · Proof & congruence/similarity
Two-column / paragraph proofs
Definition
A proof is a logical chain from given facts to a conclusion using definitions, postulates, and theorems. Two-column format lists Statements | Reasons. Paragraph proofs write the same chain in sentences.
Read this
Start by marking the diagram: givens, tick marks, parallel arrows, right angles. Write Given and Prove explicitly.
Each new statement needs a reason: given, definition, postulate (e.g. ruler/protractor), or a named theorem (vertical angles, CPCTC, etc.).
Two-column trains precision; paragraph trains fluency. Same logic either way — never skip justification.
Template: Given → immediate consequences (definitions) → bridge theorems → conclusion. Aim for the shortest clear path.
Drill with flashcards
Flip through these until you can say the answer before revealing it.
Flashcards · 1 / 4
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Try this
Attempt each problem first, then open the worked solution.
1.Prove: vertical angles are congruent (two-column).
2.Rewrite a short two-column proof as a paragraph proof.