Geometry Reasoning Proof Quiz – Free PDF

Contents

This geometry reasoning proof quiz asks 10 multiple-choice questions on logic and two-column proofs, and each answer comes with a short explanation.

Ten multiple-choice questions check conditional statements, converse and contrapositive, counterexamples, inductive and deductive reasoning, properties of equality and vertical angles (G-CO.C.9). Choose one answer, then read the explanation.

GeometryCommon Core: G-CO.C.9

🎯 Logic and Two-Column Proofs – Geometry math quiz

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Question 1

Which conditional statement does the diagram show?

Robins are inside birds.

A If an animal is a bird, then it is a robin.

B If an animal is not a bird, then it is a robin.

C If an animal is not a robin, then it is not a bird.

D If an animal is a robin, then it is a bird.

Question 2

What is the converse of “If \(x>5\), then \(x>3\)”?

A If \(x\le 5\), then \(x\le 3\).

B If \(x\le 3\), then \(x\le 5\).

C If \(x>3\), then \(x>5\).

D If \(x>5\), then \(x\le 3\).

Question 3

What is the contrapositive of “If a polygon is a triangle, then it has three sides”?

A If a polygon has three sides, then it is a triangle.

B If a polygon does not have three sides, then it is not a triangle.

C If a polygon is not a triangle, then it does not have three sides.

D If a polygon is not a triangle, then it has three sides.

Question 4

Which number is a counterexample to “If a number is odd, then it is prime”?

A 9

B 7

C 13

D 2

Question 5

Liam measures the angles of six triangles, finds that every angle sum is \(180^{\circ}\), and concludes that all triangles have that angle sum. What type of reasoning is this?

A Deductive reasoning

B Inductive reasoning

C Proof by definition

D Reasoning with a counterexample

Question 6

If \(AB=7\) and \(AB+BC=20\), then \(7+BC=20\). Which property justifies this step?

A Reflexive Property of Equality

B Symmetric Property of Equality

C Substitution Property of Equality

D Division Property of Equality

Question 7

Angles 1 and 3 are vertical angles with \(m\angle 1\)\(=(3x+5)^{\circ}\) and \(m\angle 3\)\(=(5x-15)^{\circ}\). What is x?

Angles 1 and 3 are opposite each other.

A \(x=5\)

B \(x=20\)

C \(x=40\)

D \(x=10\)

Question 8

In the proof that vertical angles are congruent, why are \(\angle 1\) and \(\angle 2\) supplementary?

Angles 1 and 2 are next to each other on a line.

A They are vertical angles.

B They form a linear pair.

C They are complementary.

D They are congruent by definition.

Question 9

What is the next number in the pattern 4, 7, 12, 19, 28?

A 39

B 37

C 35

D 41

Question 10

Which statement is a true biconditional?

A A number is even if and only if it is divisible by 4.

B An angle is acute if and only if its measure is less than 100°.

C A figure is a rectangle if and only if it is a square.

D A figure is a triangle if and only if it has exactly three sides.

🎉 Quiz complete!

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How does this quiz work?

Read each question, choose one answer among A, B, C and D, then check it: a short explanation appears after every answer. Your score out of 10 is shown at the end, and you can restart the quiz as often as you like.

What should you review before the quiz?

Reread the key facts of the lesson and the worked example. If a question is hard, go back to the matching part of the lesson, then try the quiz again. Write your work on scrap paper: most mistakes come from skipping a step, not from the idea itself.

Remember:

A conditional “If p, then q” has a hypothesis (p) and a conclusion (q).
The converse swaps p and q, the inverse negates both, and the contrapositive does both.
A statement and its contrapositive always have the same truth value.
One counterexample disproves a conditional; inductive patterns are not proofs.
Vertical angles are congruent, proved with linear pairs and the Subtraction Property of Equality.