Geometry (Grades 9–10) Midterm — Units 1–2

Math Grades 9–10 20 multiple choice + 1 written

Free printable Geometry midterm (Grades 9–10): 20 multiple-choice questions plus 1 written response covering Foundations: Points, Lines & Angles, Reasoning & Proof. Answer key included — customize it in the Midterm Maker.

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Directions: Read each question carefully and choose the best answer. Answer the written response in complete sentences.

Covers: Foundations: Points, Lines & Angles · Reasoning & Proof

Part 1: Multiple Choice

What is the midpoint of the segment with endpoints (2, -4) and (8, 6)?
1. A. (5, 1)
2. B. (5, -1)
3. C. (3, 5)
4. D. (10, 2)
M(3, 5) is the midpoint of segment AB, and A is at (1, 2). What are the coordinates of B?
1. A. (5, 8)
2. B. (2, 3.5)
3. C. (-1, -1)
4. D. (4, 7)
Ray BD bisects angle ABC. The measure of angle ABD is (2x + 10)° and the measure of angle DBC is (4x - 20)°. What is the measure of angle ABC?
1. A. 40°
2. B. 80°
3. C. 160°
4. D. 15°
M is the midpoint of segment AB. AM = 3x + 4 and MB = 5x - 6. What is AB?
1. A. 76
2. B. 19
3. C. 38
4. D. 5
Two lines intersect. A pair of vertical angles measure (5x - 10)° and (3x + 30)°. What is the measure of each of these angles?
1. A. 90°
2. B. 20°
3. C. 100°
4. D. 45°
Two angles form a linear pair. One measures 3x degrees and the other measures (x + 20) degrees. What is the measure of the larger angle?
1. A. 40°
2. B. 60°
3. C. 120°
4. D. 140°
Which three terms are undefined terms in geometry?
1. A. Segment, ray, and angle
2. B. Line, segment, and plane
3. C. Point, angle, and ray
4. D. Point, line, and plane
The supplement of an angle is three times its complement. What is the measure of the angle?
1. A. 45°
2. B. 67.5°
3. C. 60°
4. D. 22.5°
Points A, B, and C are collinear, and B is between A and C. AB = 7 and BC = 12. What is AC?
1. A. 12
2. B. 84
3. C. 5
4. D. 19
What is the distance between (-1, 2) and (5, 10)?
1. A. 8
2. B. 14
3. C. 100
4. D. 10
Given: "If it rains, then the game is canceled" and "It is raining." Which conclusion follows by the Law of Detachment?
1. A. It will stop raining.
2. B. The game is canceled.
3. C. The game is not canceled.
4. D. If the game is canceled, then it is raining.
Which pair of statements is equivalent to the biconditional "An angle is right if and only if it measures 90°"?
1. A. If an angle is right, then it does not measure 90°; if it measures 90°, then it is right.
2. B. If an angle is right, then it measures 90°; if an angle measures 90°, then it is right.
3. C. If an angle measures 90°, then it is right; if an angle is not right, then it measures 90°.
4. D. If an angle is right, then it measures 90°; if an angle is not right, then it measures 90°.
What is the converse of "If an animal is a dog, then it has four legs"?
1. A. An animal is a dog if and only if it has four legs.
2. B. If an animal is not a dog, then it does not have four legs.
3. C. If an animal has four legs, then it is a dog.
4. D. If an animal does not have four legs, then it is not a dog.
Which number is a counterexample to "If a number is prime, then it is odd"?
1. A. 9
2. B. 2
3. C. 3
4. D. 15
What is the contrapositive of "If x = 3, then x^2 = 9"?
1. A. If x^2 = 9, then x = 3.
2. B. If x^2 ≠ 9, then x ≠ 3.
3. C. If x = 3, then x^2 ≠ 9.
4. D. If x ≠ 3, then x^2 ≠ 9.
In a proof, the step "2(x + 3) = 14" is followed by "2x + 6 = 14." Which reason justifies the second step?
1. A. Reflexive Property of Equality
2. B. Distributive Property
3. C. Division Property of Equality
4. D. Subtraction Property of Equality
Use inductive reasoning to find the next number: 3, 7, 11, 15, ...
1. A. 18
2. B. 30
3. C. 21
4. D. 19
Which property justifies "If AB = CD, then CD = AB"?
1. A. Reflexive Property of Equality
2. B. Substitution Property of Equality
3. C. Symmetric Property of Equality
4. D. Transitive Property of Equality
In a proof, a student writes: "∠1 and ∠2 are vertical angles, so ∠1 ≅ ∠2." Which reason supports this step?
1. A. Definition of supplementary angles
2. B. Vertical Angles Theorem
3. C. Linear Pair Postulate
4. D. Corresponding Angles Postulate
Given: "If a figure is a square, then it is a rectangle" and "If a figure is a rectangle, then it has four right angles." Which conclusion follows by the Law of Syllogism?
1. A. If a figure is not a square, then it is not a rectangle.
2. B. If a figure is a rectangle, then it is a square.
3. C. If a figure has four right angles, then it is a square.
4. D. If a figure is a square, then it has four right angles.

Part 2: Written Response

Given: ∠1 and ∠2 form a linear pair, and ∠2 and ∠3 form a linear pair. Prove: ∠1 ≅ ∠3. Write a two-column proof with a reason for every statement.

Answer Key — Geometry (Grades 9–10) Midterm — Units 1–2

A — (5, 1) Average the coordinates: ((2 + 8)/2, (-4 + 6)/2) = (5, 1).
A — (5, 8) B = (2·3 - 1, 2·5 - 2) = (5, 8).
B — 80° 2x + 10 = 4x - 20 gives x = 15; each half is 40°, so 80°.
C — 38 3x + 4 = 5x - 6 gives x = 5; AM = 19, so AB = 38.
A — 90° Vertical angles are equal: 5x - 10 = 3x + 30 gives x = 20, so 90°.
C — 120° 3x + x + 20 = 180 gives x = 40; the angles are 120° and 60°.
D — Point, line, and plane Points, lines, and planes are described, not defined; other terms are built from them.
A — 45° 180 - a = 3(90 - a) gives 2a = 90, so a = 45.
D — 19 Segment Addition Postulate: AC = AB + BC = 19.
D — 10 √((5 - (-1))² + (10 - 2)²) = √(36 + 64) = √100 = 10.
B — The game is canceled. When the hypothesis is true, the conclusion must be true.
B — If an angle is right, then it measures 90°; if an angle measures 90°, then it is right. A biconditional combines a conditional and its converse.
C — If an animal has four legs, then it is a dog. The converse switches the hypothesis and the conclusion.
B — 2 2 is prime but even, so the statement is false.
B — If x^2 ≠ 9, then x ≠ 3. The contrapositive switches and negates both parts.
B — Distributive Property Multiplying 2 by each term inside the parentheses uses the Distributive Property.
D — 19 The pattern adds 4 each time: 15 + 4 = 19.
C — Symmetric Property of Equality The Symmetric Property lets you swap the two sides of an equation.
B — Vertical Angles Theorem The Vertical Angles Theorem states vertical angles are congruent.
D — If a figure is a square, then it has four right angles. If p → q and q → r, then p → r.

Written Response — Look-Fors

Linear Pair Postulate (both pairs supplementary); definition of supplementary angles (m∠1 + m∠2 = 180 and m∠2 + m∠3 = 180); Substitution or Transitive Property; Subtraction Property of Equality; definition of congruent angles. Final statement: ∠1 ≅ ∠3 (Congruent Supplements Theorem).

Geometry (Grades 9–10) Midterm — Units 1–2

Part 1: Multiple Choice

Part 2: Written Response

Written Response — Look-Fors

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