• 44 questions

Geometry Unit 2 Test

Tap the answer and see the reason.

See all 44 with answers
Which is a counterexample to "If x² = 49, then x = 7"?

Pick an answer, then press Check answer. Then you see Correct or Not quite, with the reason. Keys: A to D pick, Enter checks.

Print covers the next 20 questions. Share this set copies a link to the same questions in the same order.

Exam mode: 20 questions, no time limit.

More options

Unofficial practice questions, not affiliated with any school, textbook publisher or curriculum. Bank checked September 24, 2026.

Next step Later in the course: the circle geometry test

All 44 questions with answers

Conditional statements 14

  • A conditional statement is true. Which related statement must also be true? Answer: Its contrapositive. Source: Wikipedia, Contraposition. Read 2026-09-24.
  • "If a figure is a square, then it is a rectangle" is true. Is its converse true? Answer: No: a 2 × 5 rectangle is not a square. Source: Wikipedia, Converse (logic). Read 2026-09-24.
  • In "If a triangle has three equal sides, then it is equilateral," what is the conclusion? Answer: It is equilateral. Source: Wikipedia, Material conditional. Read 2026-09-24.
  • In "If two lines are perpendicular, then they form right angles," what is the hypothesis? Answer: Two lines are perpendicular. Source: Wikipedia, Material conditional. Read 2026-09-24.
  • What is the contrapositive of "If a figure is a square, then it is a rectangle"? Answer: If a figure is not a rectangle, then it is not a square. Source: Wikipedia, Contraposition. Read 2026-09-24.
  • What is the contrapositive of "If a number ends in 0, then it is divisible by 5"? Answer: If a number is not divisible by 5, then it does not end in 0. Source: Wikipedia, Contraposition. Read 2026-09-24.
Show all 44 questions (38 more)

Conditional statements, continued

  • What is the converse of "If a figure is a square, then it is a rectangle"? Answer: If a figure is a rectangle, then it is a square. Source: Wikipedia, Converse (logic). Read 2026-09-24.
  • What is the converse of "If an angle measures 90°, then it is a right angle"? Answer: If an angle is a right angle, then it measures 90°. Source: Wikipedia, Converse (logic). Read 2026-09-24.
  • What is the inverse of "If an angle measures 90°, then it is a right angle"? Answer: If an angle does not measure 90°, then it is not a right angle. Source: Wikipedia, Inverse (logic). Read 2026-09-24.
  • What is the inverse of "If two angles are vertical angles, then they are congruent"? Answer: If two angles are not vertical angles, then they are not congruent. Source: Wikipedia, Inverse (logic). Read 2026-09-24.
  • When can a conditional be written as a biconditional ("if and only if")? Answer: When the statement and its converse are both true. Source: Wikipedia, Logical biconditional. Read 2026-09-24.
  • Which is a counterexample to "If a number is prime, then it is odd"? Answer: 2. Source: Wikipedia, Counterexample. Read 2026-09-24.
  • Which is a counterexample to "If x² = 49, then x = 7"? Answer: x = −7. Source: Wikipedia, Counterexample. Read 2026-09-24.
  • Which pair of statements always have the same truth value? Answer: The converse and the inverse. Source: Wikipedia, Inverse (logic). Read 2026-09-24.

Inductive and deductive reasoning 10

  • "If a figure is a square, it has four sides. Figure F has four sides." What can you conclude? Answer: Nothing: F might not be a square. Source: Wikipedia, Modus ponens. Read 2026-09-24.
  • "If an angle is acute, it measures less than 90°. Angle A is acute." What follows by the Law of Detachment? Answer: Angle A measures less than 90°. Source: Wikipedia, Modus ponens. Read 2026-09-24.
  • "If it rains, the game is cancelled. If the game is cancelled, we go to the movies." What follows by the Law of Syllogism? Answer: If it rains, we go to the movies. Source: Wikipedia, Hypothetical syllogism. Read 2026-09-24.
  • Noticing a pattern in several examples and making a general guess is… Answer: Inductive reasoning. Source: Wikipedia, Inductive reasoning. Read 2026-09-24.
  • Use inductive reasoning: what comes next in 1, 4, 9, 16, …? Answer: 25. Source: Wikipedia, Inductive reasoning. Read 2026-09-24.
  • Use inductive reasoning: what comes next in 2, 6, 18, 54, …? Answer: 162. Source: Wikipedia, Inductive reasoning. Read 2026-09-24.
  • Use inductive reasoning: what comes next in 3, 7, 11, 15, …? Answer: 19. Source: Wikipedia, Inductive reasoning. Read 2026-09-24.
  • Use inductive reasoning: what comes next in 5, 3, 1, -1, …? Answer: -3. Source: Wikipedia, Inductive reasoning. Read 2026-09-24.
  • Using definitions, facts and rules to reach a conclusion that must be true is… Answer: Deductive reasoning. Source: Wikipedia, Deductive reasoning. Read 2026-09-24.
  • Why does inductive reasoning not prove a statement? Answer: One counterexample could still show it false. Source: Wikipedia, Inductive reasoning. Read 2026-09-24.

Properties of equality 10

  • From 2(x + 3) = 16 to 2x + 6 = 16. Which property justifies the step? Answer: Distributive property. Source: Wikipedia, Distributive property. Read 2026-09-24.
  • From 5x = 35 to x = 7. Which property justifies the step? Answer: Division property of equality. Source: Wikipedia, Equality (mathematics). Read 2026-09-24.
  • From x + 4 = 10 to x = 6. Which property justifies the step? Answer: Subtraction property of equality. Source: Wikipedia, Equality (mathematics). Read 2026-09-24.
  • From x − 7 = 12 to x = 19. Which property justifies the step? Answer: Addition property of equality. Source: Wikipedia, Equality (mathematics). Read 2026-09-24.
  • From x/3 = 8 to x = 24. Which property justifies the step? Answer: Multiplication property of equality. Source: Wikipedia, Equality (mathematics). Read 2026-09-24.
  • If AB = CD and CD = EF, then AB = EF. Which property is this? Answer: Transitive property. Source: Wikipedia, Equality (mathematics). Read 2026-09-24.
  • If m∠A = m∠B, then m∠B = m∠A. Which property is this? Answer: Symmetric property. Source: Wikipedia, Equality (mathematics). Read 2026-09-24.
  • If x = 5 and y = x + 2, then y = 5 + 2. Which property is this? Answer: Substitution property. Source: Wikipedia, Equality (mathematics). Read 2026-09-24.
  • Solve 5x + 6 = 36. Which pair of steps and reasons is right? Answer: Subtract 6 (subtraction property), then divide by 5 (division property): x = 6. Source: Wikipedia, Equality (mathematics). Read 2026-09-24.
  • Which property says AB = AB? Answer: Reflexive property. Source: Wikipedia, Equality (mathematics). Read 2026-09-24.

Reasons in proofs 10

  • ∠1 and ∠2 form a linear pair. Which reason gives m∠1 + m∠2 = 180°? Answer: Linear Pair Postulate (they are supplementary). Source: Wikipedia, Angle. Read 2026-09-24.
  • ∠1 and ∠3 are both complementary to ∠2. What follows? Answer: ∠1 ≅ ∠3 (complements of the same angle are congruent). Source: Wikipedia, Angle. Read 2026-09-24.
  • B lies on AC between A and C. Which reason gives AB + BC = AC? Answer: Segment Addition Postulate. Source: Wikipedia, Line segment. Read 2026-09-24.
  • D lies inside ∠ABC. Which reason gives m∠ABD + m∠DBC = m∠ABC? Answer: Angle Addition Postulate. Source: Wikipedia, Angle. Read 2026-09-24.
  • In a two-column proof, what goes in the right-hand column? Answer: The reason for each statement. Source: Wikipedia, Mathematical proof. Read 2026-09-24.
  • M is the midpoint of AB. Which reason gives AM = MB? Answer: Definition of midpoint. Source: Wikipedia, Midpoint. Read 2026-09-24.
  • Two angles of a linear pair measure (3x + 5)° and (x + 15)°. What is x, and which reason sets up the equation? Answer: x = 40, by the Linear Pair Postulate. Source: Wikipedia, Angle. Read 2026-09-24.
  • Vertical angles measure (5x − 18)° and (3x + 34)°. What is x? Answer: 26. Source: Wikipedia, Angle. Read 2026-09-24.
  • What is a statement accepted as true without proof called? Answer: A postulate (axiom). Source: Wikipedia, Axiom. Read 2026-09-24.
  • Which theorem says vertical angles are congruent? Answer: The Vertical Angles Theorem. Source: Wikipedia, Angle. Read 2026-09-24.

How this list was compiled: Questions, wrong choices and explanations were written for this site. Logic and proof terms were checked on Wikipedia (Material conditional, Converse, Inverse, Contraposition, Logical biconditional, Counterexample, Inductive reasoning, Deductive reasoning, Modus ponens, Hypothetical syllogism, Equality, Distributive property, Angle, Axiom), each named in the question's source line and read 2026-09-24. Every number was calculated. Licence: own work

How it works

This geometry unit 2 test review has 44 questions on reasoning and proof: conditional statements and their converse, inverse and contrapositive, inductive and deductive reasoning, properties of equality, and the reasons used in proofs.

Read the full guide

Four sets

Conditional statements covers hypothesis, conclusion, converse, inverse, contrapositive and counterexamples. Reasoning covers patterns and the laws of detachment and syllogism. Properties of equality names each algebra step. Reasons in proofs gives the postulate or theorem.

Before the test

Practice brings a missed question back until you get it right. After a round, Print lists its questions: remove one, add more up to all 44, and tick With answer key.

  • Converse: swap. Inverse: negate. Contrapositive: swap and negate.
  • A statement and its contrapositive are always both true or both false.
  • One counterexample is enough to show a conditional is false: 2 is a prime that is not odd.

Questions and answers

What is on a geometry unit 2 test?

In many courses, reasoning and proof: conditional statements, converse, inverse and contrapositive, biconditionals, inductive and deductive reasoning, properties of equality, and two-column proofs about segments and angles. Your course's own list comes first.

What is the difference between the converse and the contrapositive?

The converse swaps the hypothesis and conclusion. The contrapositive swaps them and negates both. The contrapositive always shares the truth value of the original; the converse may not.

What is the Law of Syllogism?

If p → q and q → r are both true, then p → r is true. The Law of Detachment says: if p → q is true and p is true, q must be true.

More quizzes

Show 6 more

Browse Science Quizzes