SAT Math / Topic

Geometry and Trigonometry

Geometry and Trigonometry is about 15% of SAT Math: angle relationships, triangles and similarity, circles, area and volume, coordinate geometry, and right-triangle trig. A reference sheet of common formulas is provided, but speed comes from knowing them cold.

53 practice questions22 skill areas

What the exam asks

  • Use angle relationships from parallel lines, triangles, and polygons
  • Apply the Pythagorean theorem and recognize special right triangles
  • Work with similar triangles and scale factors for lengths and areas
  • Compute arc length, sector area, and interpret circle equations
  • Solve right triangles with sine, cosine, and tangent
  • Use distance, midpoint, and slope in the coordinate plane

Key formulas and rules

Pythagorean theorem

a² + b² = c²

Special right triangles

45-45-90: x, x, x√2; 30-60-90: x, x√3, 2x

SOHCAHTOA

sin = opp/hyp, cos = adj/hyp, tan = opp/adj

Complementary angles

sin(x) = cos(90° − x)

Circle equation

(x − h)² + (y − k)² = r², center (h, k), radius r

Arc and sector

arc = (θ/360)·2πr, sector = (θ/360)·πr²

Triangle angle sum

interior angles sum to 180°; exterior angle = sum of remote interior angles

Question bank breakdown

Multiple choice

53

Difficulty mix

15 easy · 19 medium · 19 hard

Skills covered

Area, perimeter, volumeAngles, triangles, Pythagorean theoremCircle theorems (area, arc, sector, equations)Coordinate geometry (distance, midpoint, parallel/perpendicular)Right triangle trigonometry (sin, cos, tan)Similar triangles, congruenceAreaVolumeSurface areaTriangle angle relationshipsLines and anglesPythagorean theoremTrigonometric ratiosRight trianglesEquation of a circleCentral angles and arcsArc lengthSector areaRadians and degreesSimilar trianglesTrigonometry in similar right trianglesUnit circle basics

Every question in the bank comes with a worked explanation, and most add a per-choice breakdown so you learn why each wrong answer is wrong - not just the key.

Sample question

From the free tier of the ScoreMint SAT Math bank - try it, then check the answer.

A right circular cylinder has a radius of 4 cm and a height of 9 cm. A second right circular cylinder has a radius of 6 cm and the same volume as the first cylinder. What is the height, in cm, of the second cylinder?

  • A. 4
  • B. 6
  • C. 3
  • D. 2.5
Show answer and explanation

Answer: A. Correct. V₁ = π(4²)(9) = 144π. For the second: 144π = π(6²)(h₂) = 36πh₂. So h₂ = 144/36 = 4. Check: π(36)(4) = 144π ✓.

Study tip

Similar-triangle questions hide in wordy setups (shadows, ramps, nested triangles). The moment two triangles share two angles, set up a side ratio - that single move solves most SAT geometry word problems.