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Quizzes > Mathematics

Two column proof practice quiz for high school geometry

20 quick questions with instant results-sharpen your geometric proof practice

Editorial: Review CompletedCreated By: Jesus SerranoUpdated Aug 23, 2025
Difficulty: Moderate
Grade: Grade 9
Study OutcomesCheat Sheet
Paper art representing a trivia quiz about the Column Proof Challenge for geometry students.

This quiz helps you practice writing clear two-column proofs, build speed, and check your reasoning with instant results. Review angle relationships with our parallel lines and transversals quiz, boost logic with the inductive and deductive reasoning quiz, and wrap up with a quick tune-up using the geometry review quiz.

Which postulate justifies that if m∠ABC + m∠CBD = m∠ABD, then point C lies in the interior of ∠ABD?
Corresponding Angles Postulate
Triangle Sum Theorem
Angle Addition Postulate - because it states the whole angle equals the sum of its non-overlapping parts
Linear Pair Postulate
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From AB = BC and BC = CD, what can you conclude to use in a proof?
AB = CD - because equality is transitive
AB = AD
BD = AC
AB = AC
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Vertical angles are congruent.
False
True
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If a transversal crosses parallel lines, which angle pair is always congruent?
Exterior angles on the same side of the transversal
Consecutive interior angles
Corresponding angles - because parallel lines cut by a transversal create congruent corresponding angles
Linear pair angles
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Angles that form a linear pair are supplementary.
True
False
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In any triangle, the largest angle is opposite the shortest side.
True
False
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Which postulate can prove triangle congruence from three pairs of equal sides?
SSS - because three corresponding sides determine a triangle
ASA
AAS
HL
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The diagonals of every kite are congruent.
False
True
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Which theorem justifies that an exterior angle of a triangle equals the sum of the two remote interior angles?
Triangle Sum Theorem
Parallel Postulate
Isosceles Triangle Theorem
Exterior Angle Theorem - because the exterior angle equals the sum of the two non-adjacent interior angles
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If two angles are congruent, their supplements are congruent.
False
True
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Given triangles are right and have a hypotenuse and one leg congruent, which method proves triangle congruence?
HL - because right triangles are congruent if hypotenuse and a leg are congruent
SSA
AAS
ASA
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The sum of the measures of the interior angles of any triangle is 180 degrees.
False
True
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Which justification shows that if m∠1 = m∠2, then m∠1 + m∠3 = m∠2 + m∠3?
Distributive Property
Transitive Property
Addition Property of Equality - because adding the same measure to equal measures preserves equality
Subtraction Property of Equality
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The midpoint of a segment is the point that divides it into two segments of equal length and equal measure.
False
True
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Which theorem states that if a transversal cuts two parallel lines, then same-side interior angles are supplementary?
Corresponding Angles Postulate
Isosceles Triangle Theorem
Consecutive Interior Angles Theorem - because same-side interior angles sum to 180 with parallel lines
Vertical Angles Theorem
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Which choice is a valid reason to move from 5(x - 2) = 10 to 5x - 10 = 10 in a proof?
Addition Property of Equality
Reflexive Property
Distributive Property - because a(b - c) = ab - ac
Multiplication Property of Equality
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If two angles are supplementary and congruent, each must be a right angle.
False
True
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Which condition is NOT sufficient to prove triangle congruence?
SAS
ASA
SSS
SSA - because side-side-angle is ambiguous without a right angle
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A median of a triangle always forms two isosceles triangles.
True
False
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In a proof, from AB = CD you deduce AB + EF = CD + EF. Which property is used?
Division Property of Equality
Symmetric Property
Substitution Property
Addition Property of Equality - because adding equal quantities preserves equality
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Study Outcomes

  1. Construct step-by-step two-column proofs to demonstrate logical reasoning.
  2. Apply geometric postulates and theorems in structured proof formats.
  3. Analyze given statements to identify valid reasoning in column proofs.
  4. Evaluate the logical flow of arguments to determine the correctness of a proof.
  5. Demonstrate proficiency in organizing and presenting mathematical proofs clearly.

Two Column Proofs Review Cheat Sheet

  1. Understand the Structure of Two-Column Proofs - Think of two-column proofs as your crime scene board: on the left, you pin down each statement; on the right, you match it with a solid reason. This clear layout guides your logical journey from what's given to the grand finale conclusion.
  2. Master Key Geometric Postulates and Theorems - Postulates like Side-Angle-Side (SAS) and Angle-Side-Angle (ASA) are your trusty tools in the proof workshop. Get cozy with these foundational rules, because they'll be your best friends when you need to prove two shapes are twins.
  3. Practice Writing Proofs for Triangle Congruence - Triangles rule the proof world, and congruence postulates are your secret codes to crack them open. By practicing several triangle congruence proofs, you'll see patterns and shortcuts emerge, making every new challenge feel familiar.
  4. Utilize Visual Aids to Comprehend Proofs - Diagrams are like maps for your proof journey - they show you where you've been and where you're headed. A lively sketch can bridge the gap between abstract statements and concrete understanding, turning "huh?" into "aha!" in no time.
  5. Learn Strategies for Proving Parallelograms - Proving a quadrilateral is a parallelogram can feel like proving a celebrity's identity - show those opposite sides are parallel or congruent and you'll nail it. Mix and match different approaches to see which proof style plays to your strengths.
  6. Develop a Game Plan for Proofs - Before diving in, sketch a quick outline that connects your givens to your goal - this pre-proof pep talk keeps you on track. Having a roadmap means fewer "Uh-oh" moments and more confident steps toward that satisfying Q.E.D.
  7. Practice with Step-by-Step Proof Tutorials - Guided tutorials are like having a proof coach whispering tips in your ear. Follow each step closely, then try replicating the logic on your own problems to build unstoppable proof muscles.
  8. Understand the Importance of Justifying Each Step - Every statement in your proof needs a rock-solid reason, whether it's a definition, postulate, or a previously proven theorem. Skipping justifications is like leaving plot holes in a mystery novel - your proof won't hold up under scrutiny!
  9. Work on Proofs Involving Parallel Lines and Angles - Parallel lines and transversals spawn a party of angle relationships - alternate interior, corresponding, you name it. Mastering these angle rules is like unlocking cheat codes that make complex proofs a breeze.
  10. Review Common Proof Techniques and Properties - The Reflexive, Symmetric, and Transitive properties of equality pop up everywhere in proofs - consider them your proof power-ups. Keeping these properties at your fingertips means you'll breeze through many standard proof steps.
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