Logic and Two-Column Proofs: Geometry Math Quiz – PDF Download
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.
AIf an animal is a bird, then it is a robin.
BIf an animal is not a bird, then it is a robin.
CIf an animal is not a robin, then it is not a bird.
DIf an animal is a robin, then it is a bird.
Question 2
What is the converse of “If \(x>5\), then \(x>3\)”?
AIf \(x\le 5\), then \(x\le 3\).
BIf \(x\le 3\), then \(x\le 5\).
CIf \(x>3\), then \(x>5\).
DIf \(x>5\), then \(x\le 3\).
Question 3
What is the contrapositive of “If a polygon is a triangle, then it has three sides”?
AIf a polygon has three sides, then it is a triangle.
BIf a polygon does not have three sides, then it is not a triangle.
CIf a polygon is not a triangle, then it does not have three sides.
DIf 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”?
A9
B7
C13
D2
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?
ADeductive reasoning
BInductive reasoning
CProof by definition
DReasoning with a counterexample
Question 6
If \(AB=7\) and \(AB+BC=20\), then \(7+BC=20\). Which property justifies this step?
AReflexive Property of Equality
BSymmetric Property of Equality
CSubstitution Property of Equality
DDivision 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.
AThey are vertical angles.
BThey form a linear pair.
CThey are complementary.
DThey are congruent by definition.
Question 9
What is the next number in the pattern 4, 7, 12, 19, 28?
A39
B37
C35
D41
Question 10
Which statement is a true biconditional?
AA number is even if and only if it is divisible by 4.
BAn angle is acute if and only if its measure is less than 100°.
CA figure is a rectangle if and only if it is a square.
DA figure is a triangle if and only if it has exactly three sides.
🎉 Quiz complete!
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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.
