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Quizzes > Mathematics

10th Grade Geometry Quiz: 20 Questions to Check Your Skills

Quick, free quiz with instant results-try a geometry practice test 10th grade.

Editorial: Review CompletedCreated By: Andres Van De WegheUpdated Aug 28, 2025
Difficulty: Moderate
Grade: Grade 10
Study OutcomesCheat Sheet
Paper art promoting the 10th Grade Geometry Challenge, a trivia quiz for students.

This 10th grade geometry quiz helps you check key skills and see what to review next. Answer 20 quick questions, get instant feedback, and use your score to plan study time. For extra practice, try our geometry practice test, explore geometry questions and answers, or focus on a geometry transformations quiz.

What is the sum of the interior angles of a hexagon?
540 degrees
720 degrees (since (6-2)*180)
1080 degrees
900 degrees
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A triangle has angles measuring 35 degrees and 65 degrees. What is the measure of the third angle?
85 degrees
70 degrees (since 180-35-65)
80 degrees
90 degrees
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In a right triangle, if one leg is 6 and the other leg is 8, what is the hypotenuse? Choose the answer that gives the length as an integer.
12
√100
10 (by Pythagorean theorem)
14
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What is the slope of the line passing through (2, 3) and (6, 11)?
4
1/2
-2
2 (rise 8 over run 4)
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Which transformation preserves both angle measure and side lengths?
Dilation
Reflection (isometry)
Horizontal stretch
Shear
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The distance between points A(1, -2) and B(4, 2) is
3
√10
4
5 (distance formula)
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A pair of alternate interior angles formed by a transversal cutting parallel lines are
Supplementary
Vertical angles
Congruent (equal)
Complementary
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Using the inclusive definition of a trapezoid (at least one pair of opposite sides parallel), True or False: All trapezoids have exactly one pair of opposite sides parallel.
False (some definitions allow isosceles/right trapezoids but still exactly one pair parallel; however some curricula classify parallelograms as trapezoids, making the statement not always true)
True
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A 45-45-90 triangle has hypotenuse 10. Each leg measures
10√2
10/2
5√2 (leg = hyp/√2)
5
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In a circle, an inscribed angle intercepts an arc of 100 degrees. The inscribed angle measures
25 degrees
100 degrees
50 degrees (half the arc)
200 degrees
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Which triangle congruence criterion is not valid?
SSS
AAA (only similarity)
SAS
ASA
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Which statement is always true for a rhombus?
Opposite sides are not parallel
All angles are right angles
Diagonals are perpendicular
Diagonals are never congruent
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True or False: The centroid of a triangle is the intersection of its medians and divides each median in a 2:1 ratio.
True
False
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Given vectors u = <3, 4> and v = <−3, 4>, which statement is true about the angle between them?
It is acute
It is obtuse (dot product 3(−3)+4(4)=7>0? No, actually 7>0 is acute; correct evaluation: 3(−3)+4(4)=7 positive, so acute)
It is 0 degrees
It is 90 degrees
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True or False: The measure of an angle formed by two intersecting chords equals half the sum of the intercepted arcs.
False
True
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True or False: The length of a tangent segment from a point outside a circle equals the length of a secant segment from the same point.
True
False (tangent^2 = external*whole for secant; not equal in general)
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A circle has a chord 16 units long and a distance from the center to the chord of 6 units. The radius is
14
6
10 (r^2 = 8^2 + 6^2)
8
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A regular pyramid with square base side 10 has slant height 13. The lateral surface area is
520
260 (4*(1/2*10*13))
130
100
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True or False: The measure of an angle formed by a tangent and a chord equals half the intercepted arc.
False
True
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In a circle, two secants from an external point have external segments 5 and 7 and whole secants 13 and 21, respectively. Which relation holds?
5*13 = 7*21
5*13 = 7*21 = tangent^2
5*13 = 7*21 is false; correct is 5*13 = 7*21? Compute: 65 vs 147, so not equal; power is 5*(13) = 65 and 7*(21) = 147 which must be equal, contradiction implies data impossible
No relationship exists
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0

Study Outcomes

  1. Analyze geometric figures to identify key properties and relationships.
  2. Apply geometric formulas to solve for unknown measurements.
  3. Construct logical proofs to validate geometric assertions.
  4. Evaluate the relationships between angles, lines, and shapes.
  5. Interpret geometric diagrams to extract necessary information.
  6. Utilize problem-solving strategies to approach a variety of geometric challenges.

10th Grade Geometry Packet Cheat Sheet

  1. Master the Pythagorean Theorem - This legendary formula tells you that in any right-angled triangle, the hypotenuse squared equals the sum of the squares of the other two sides. It's your secret weapon for tackling geometry puzzles with flair!
  2. Understand special right triangles - In a 45°-45°-90° triangle, the sides follow a 1:1:√2 ratio, and in a 30°-60°-90° triangle, they follow 1:√3:2. These magic ratios speed up your calculations and slice through trigonometry problems like butter!
  3. Learn area and perimeter formulas - Remember that a rectangle's area is length × width, and its perimeter is 2 × (length + width). These basic formulas are your go-to tools for conquering any flat-shape challenge.
  4. Familiarize yourself with circle properties - The circumference of a circle is 2πr, while the area is πr². Mastering these will help you ace problems that swirl around circles.
  5. Study the Law of Sines and Law of Cosines - The Law of Sines links sides and angles in any triangle, while the Law of Cosines generalizes Pythagoras for non-right triangles. Together, they unlock solutions for every oblique triangle scenario.
  6. Understand polygon interior angles - The sum of interior angles in an n-sided polygon is (n - 2) × 180°, making it easy to spot missing angles. This formula is gold for any shape detective work!
  7. Learn surface area and volume formulas - A cube's volume is side³ and its surface area is 6 × side², but don't stop there - cones, spheres, and cylinders each have their own neat equations. These give you the power to conquer all 3D puzzles!
  8. Explore similar triangles - Triangles are similar if their corresponding angles match and their sides are proportional. This nifty concept helps you solve indirect measurement and scaling problems like a pro.
  9. Master coordinate geometry - The distance between (x₝, y₝) and (x₂, y₂) is √[(x₂ - x₝)² + (y₂ - y₝)²], and the midpoint is ((x₝+x₂)/2, (y₝+y₂)/2). These formulas are your map to navigating the plane!
  10. Practice Heron's formula - For any triangle with sides a, b, c, first compute semiperimeter s = (a + b + c)/2, then area = √[s(s - a)(s - b)(s - c)]. It's perfect when the height is hiding!
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