Two-column Proofs Logic Test – Geometry Math (Printable PDF)

Question 1 Converse and contrapositive (2 points)

Consider the statement: “If a whole number is divisible by 6, then it is divisible by 3.”

1. Write the converse. (1 point)
2. Write the contrapositive. (1 point)

Question 2 Types of reasoning (2 points)

Label each argument inductive or deductive and explain in one sentence.

1. A city bus arrived at 7:42 a.m. every school day for five weeks, so a rider concludes it always arrives at 7:42. (1 point)
2. Every square has four right angles. Shape WXYZ is a square. So WXYZ has four right angles. (1 point)

Question 3 Properties of equality (2 points)

Identify the property of equality behind each statement.

1. If 3x = 24, then x = 8. (1 point)
2. If ∠A ≅ ∠B and ∠B ≅ ∠C, then ∠A ≅ ∠C. (1 point)

Question 4 Solve and justify (3 points)

Solve 3(x + 4) − 7 = 2x + 15 and give a reason for every step.

Question 5 Quarter of a segment (4 points)

Given: M is the midpoint of AB, and N is the midpoint of AM. Prove: AN = ¼AB. Complete a two-column proof.

Question 6 Vertical angles (3 points)

Two lines intersect. A pair of vertical angles measures (9x − 14)° and (6x + 16)°.

1. Find x. (1 point)
2. Find the measure of each vertical angle. (1 point)
3. Find the measure of a neighboring angle. (1 point)

Question 7 Using a true statement (2 points)

Assume the statement “If a shape is a square, then it is a rectangle” is true.

1. Shape ABCD is not a rectangle. What can be concluded? (1 point)
2. Shape PQRS is a rectangle. Can it be concluded that PQRS is a square? Explain. (1 point)

Question 8 Counterexamples (2 points)

Give a counterexample for each statement.

1. If x² > 9, then x > 3. (1 point)
2. If two angles are congruent, then they are vertical angles. (1 point)