Two-column Proofs Logic Quiz – Geometry (10 Questions)

Last updated: October 22, 2026 · Written by the Math Made Easy math teachers

Standards: G-CO.C.9 · Level: Grade 10 Geometry

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What this Reasoning, Logic and Two-Column Proofs quiz checks

• A conditional is false when one counterexample makes p true and q false.
• A conditional and its contrapositive are always true or false together.
• Inductive reasoning finds patterns; deductive reasoning proves them.
• Every step of a proof needs a reason: given, definition, postulate, theorem or property.
• Vertical angles are congruent, proved with two linear pairs.

The 10 questions of the quiz

1. What is the converse of “If it is Saturday, then the shop is closed”?
2. Which rewritten form is guaranteed to be true exactly when the original is true?
3. Which value disproves “If a number is a multiple of 3, then it is odd”?
4. Mia tests a rule on six cases and concludes it always works. What kind of reasoning is this?
5. Which property justifies “If x + 4 = 11, then x = 7″?
6. Two lines cross and a pair of vertical angles measures (3x + 8)° and (5x − 20)°. What does each of those angles measure?
7. Points A, B, C, D are in order on a line, with AB = CD. Which property justifies AB + BC = CD + BC?
8. ∠1 and ∠2 form a linear pair, so m∠1 + m∠2 = 180°. What is the reason?
9. What is the contrapositive of “If a shape is a hexagon, then it has six sides”?
10. Rule: “If a team wins, then it advances.” The Hawks did not advance. What follows?

After the quiz

Missed a question? Reread the Reasoning, Logic and Two-Column Proofs lesson, then take the quiz again. Next, solve the Geometry worksheet on Reasoning, Logic and Two-Column Proofs, one star first, then two and three stars. Finally, take the chapter test under real conditions, without notes and with a timer.