Free Praxis Geometry test Practice Questions

Sample Practice Questions

Try these 10 sample questions from the Praxis Geometry test practice bank. Each includes the answer and explanation. Continue with the interactive practice above to review the full question set.

1. 1A triangle has interior angles measuring (2x + 10)°, (3x − 5)°, and (x + 25)°. What is the measure of its largest angle?

   1. A.50°
   2. B.60°
   3. C.70°Correct answer: C
   4. D.80°

   Explanation: The source states that "measures of interior angles of a triangle sum to 180°". Thus 6x + 30 = 180, so x = 25. The angles are 60°, 70°, and 50°; the largest is 70°.

   Reference: NYSED: Geometry Overview — Congruence, G.CO.C.10

2. 2A point (x, y) lies on y = −2x and satisfies x < 0. In which quadrant must the point lie?

   1. A.Quadrant I
   2. B.Quadrant III
   3. C.Quadrant IICorrect answer: C
   4. D.Quadrant IV

   Explanation: The official explanation states that when the x-coordinate is negative and the y-coordinate positive, "the point lies in quadrant II." Here x < 0 implies y = −2x > 0, so the point has exactly that sign pattern.

   Reference: ETS: Geometry (5163) Study Companion — Page 23, Answers, explanation 12

3. 3In triangle ABC, AB = AC and angle A measures 44°. What is the measure of angle B?

   1. A.44°
   2. B.68°Correct answer: B
   3. C.88°
   4. D.136°

   Explanation: The source states that "base angles of isosceles triangles are congruent". Angles B and C are equal, and the triangle angle sum gives B = (180° − 44°)/2 = 68°.

   Reference: NYSED: Geometry Overview — Congruence, G.CO.C.10

4. 4What is the straight-line distance between A(−2, −1) and B(4, 7)?

   1. A.10Correct answer: A
   2. B.14
   3. C.2√7
   4. D.100

   Explanation: The derivation instructs, "Use the Pythagorean Theorem, c2 = a2 + b2". The horizontal and vertical changes are 6 and 8. Thus AB = √(6² + 8²) = 10. Adding the coordinate changes gives a path along two perpendicular segments, not the straight-line distance.

   Reference: ACCESS: Segment Addition and Distance — Derive the Distance Formula

5. 5D and E are the midpoints of sides AB and AC of triangle ABC. If BC = 18, which statement must hold?

   1. A.DE is parallel to BC and DE = 9.Correct answer: A
   2. B.DE is perpendicular to BC and DE = 9.
   3. C.DE is parallel to BC and DE = 18.
   4. D.DE is perpendicular to BC and DE = 18.

   Explanation: The source states that "the segment joining midpoints of two sides of a triangle is parallel to the third side and half the length". Therefore DE is parallel to BC, and DE = 18/2 = 9.

   Reference: NYSED: Geometry Overview — Congruence, G.CO.C.10

6. 6The midpoint of AB is M(1, −2), and A is (−8, 3). What are the coordinates of B?

   1. A.(−3.5, 0.5)
   2. B.(−6, −1)
   3. C.(9, −5)
   4. D.(10, −7)Correct answer: D

   Explanation: A midpoint "divides the segment into two congruent segments." Therefore its coordinates are the averages of the endpoint coordinates: (−8 + xB)/2 = 1 and (3 + yB)/2 = −2. Solving gives B(10, −7), which places M halfway from A to B.

   Reference: ACCESS: Segment Partitions and Midpoint — Midpoint

7. 7An exterior angle of a triangle is 128°. One of its two remote interior angles is 53°. Find the other remote interior angle.

   1. A.22°
   2. B.52°
   3. C.75°Correct answer: C
   4. D.105°

   Explanation: The source states that "an exterior angle of a triangle is equal to the sum of the two non‐adjacent interior angles of the triangle." Subtracting the known remote interior angle from the exterior angle gives 128° − 53° = 75°. The value 52° is the adjacent interior angle, not the requested remote angle.

   Reference: NYSED: Geometry Overview — Congruence, G.CO.C.10, NYSED example

8. 8What is the slope of the line through (−3, 4) and (5, −2)?

   1. A.positive four-thirds
   2. B.negative three-fourthsCorrect answer: B
   3. C.negative four-thirds
   4. D.positive three-fourths

   Explanation: The slope formula is displayed as "m=y2−y1x2−x1." This represents (y2 − y1)/(x2 − x1), giving (−2 − 4)/(5 − (−3)) = −6/8 = −3/4. Reversing only one difference changes the sign; interchanging rise and run gives the reciprocal.

   Reference: OpenStax: Intermediate Algebra 2e—Slope of a Line — Section 3.2, Slope of a line between two points

9. 9The diagonals AC and BD of parallelogram ABCD intersect at E. If AE = 3t − 1 and EC = t + 7, what is AC?

   1. A.4
   2. B.11
   3. C.18
   4. D.22Correct answer: D

   Explanation: The source states that "the diagonals of a parallelogram bisect each other". Consequently 3t − 1 = t + 7, so t = 4. Each half of AC is 11, and AC = 22.

   Reference: NYSED: Geometry Overview — Congruence, G.CO.C.11

10. 10Which line is parallel to, and distinct from, 3x − 2y = 8?

    1. A.y equals negative two-thirds times x plus 5.
    2. B.y equals negative three-halves times x plus 5.
    3. C.y equals positive three-halves times x plus 5.Correct answer: C
    4. D.y equals positive two-thirds times x plus 5.

    Explanation: The source states, "Parallel lines have the same slope and different y-intercepts." The given equation is y = (3/2)x − 4. Only y = (3/2)x + 5 has its slope and a different intercept.

    Reference: OpenStax: Intermediate Algebra 2e—Slope of a Line — Use Slopes to Identify Parallel and Perpendicular Lines—Parallel Lines definition