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Quantitative: Geometry for the GRE Exam

Geometry constitutes approximately 15–20% of GRE Quantitative Reasoning. The GRE does not provide a formula sheet, so key formulas must be memorised. The most tested areas are: triangle properties (angle sum, Pythagorean theorem, special right triangles 30-60-90 and 45-45-90), circle properties (circumference, area, arc length, sector area), coordinate geometry (slope, midpoint, distance), and angle relationships (parallel lines, transversals, vertical angles). GRE geometry figures are drawn to scale unless otherwise noted.

ETS GRE General Test Preparation — Quantitative Reasoning content specifications.

Locale-specific study guides

Pass-rate data, regulatory context, and study tips for Quantitative: Geometry all change by candidate locale. Pick your context:

Common failure modes

These are the patterns that cause most candidates to lose marks on this topic. Recognising them in advance is half the work.

  • !Not memorising the 30-60-90 and 45-45-90 special right triangle ratios — these save significant time on test day
  • !Confusing diameter with radius — a systematic error that doubles or halves answers
  • !Forgetting that GRE geometry figures ARE drawn to scale — you can use visual estimation to eliminate unreasonable answer choices
  • !Not applying the inscribed angle theorem correctly (inscribed angle = half the central angle subtending the same arc)

Study tips

  • 1Create a geometry formula card and memorise it: area of triangle (½bh), area of circle (πr²), circumference (2πr), arc length (θ/360 × 2πr), sector area (θ/360 × πr²), Pythagorean theorem (a²+b²=c²).
  • 2Drill the special right triangles: 30-60-90 sides are x : x√3 : 2x; 45-45-90 sides are x : x : x√2. These appear in disguised form in many coordinate geometry and circle problems.
  • 3For coordinate geometry, always find slope before applying distance or midpoint formulas — slope relationships tell you what type of quadrilateral or triangle you're dealing with.
  • 4Practice finding angles in parallel-line transversal figures: corresponding angles are equal; alternate interior angles are equal; co-interior (same-side interior) angles are supplementary.

Sample GRE Quantitative: Geometry questions

These sample items mirror the format and difficulty of real GRE questions. Practice with thousands more on the free Koydo question bank.

  1. 1

    A circle has a radius of 6. What is the area of a sector with a central angle of 60°?

    • A6πCorrect
    • B2π
    • C3π
    • D36π
    Why this answer?

    Sector area = (θ/360) × πr² = (60/360) × π × 36 = (1/6) × 36π = 6π. This requires the sector area formula and careful fraction simplification. (Illustrative.)

  2. 2

    In right triangle ABC with the right angle at C, AC = 5 and BC = 12. What is the length of the hypotenuse AB?

    • A13Correct
    • B17
    • C√119
    • D7
    Why this answer?

    AB = √(AC² + BC²) = √(25 + 144) = √169 = 13. This is the 5-12-13 Pythagorean triple — one of the most commonly tested GRE geometry facts. Memorizing common Pythagorean triples (3-4-5, 5-12-13, 8-15-17) saves time.

  3. 3

    Line l has a slope of 2/3. What is the slope of a line perpendicular to line l?

    • A3/2
    • B−2/3
    • C−3/2Correct
    • D2/3
    Why this answer?

    Perpendicular lines have slopes that are negative reciprocals of each other. The negative reciprocal of 2/3 is −3/2. This is a fundamental coordinate geometry fact: m₁ × m₂ = −1 for perpendicular lines.

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