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.
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
a² + b² = c²
45-45-90: x, x, x√2; 30-60-90: x, x√3, 2x
sin = opp/hyp, cos = adj/hyp, tan = opp/adj
sin(x) = cos(90° − x)
(x − h)² + (y − k)² = r², center (h, k), radius r
arc = (θ/360)·2πr, sector = (θ/360)·πr²
interior angles sum to 180°; exterior angle = sum of remote interior angles
Question bank breakdown
53
15 easy · 19 medium · 19 hard
Skills covered
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.