M4 Lines, angles, and triangles
One of the SAT's published Math skills, inside Geometry & Trigonometry. 74 questions here, across 17 distinct question types.
Geometry and Trigonometry on the SAT covers lines and angles, triangles, circles, area and volume, the Pythagorean theorem, and right-triangle trigonometry with sine, cosine, and tangent. Many problems reward knowing a few key relationships and drawing a clear diagram. One concrete tip: when a figure isn't given, sketch one and label everything you know, because seeing the relationships often makes the path to the answer obvious. On this page you'll find a short lesson on the essential geometry formulas and trig ratios with worked examples, plus free interactive practice with instant explanations so you can recognize common setups fast and apply the right relationship without second-guessing.
Lesson
Geometry & Trig is one of the two smallest Math domains — 5–7 of the 40 scored questions (about 15%), the same share as Problem-Solving & Data Analysis — but it shows up reliably: triangles, circles, angles, area/volume, similarity, and right-triangle trig. Memorizing a short list of formulas makes these quick.
Keep these instant
- Pythagorean: a² + b² = c². Recognize the 3-4-5 and 5-12-13 triples on sight.
- Circle: area = πr², circumference = 2πr. Arc length and sector area scale with (central angle / 360).
- Triangle angles sum to 180°. Similar triangles → sides in proportion.
- SOH-CAH-TOA: sin = opp/hyp, cos = adj/hyp, tan = opp/adj.
- Radians: 180° = π radians. Multiply degrees by π/180 to convert.
Worked examples
A right triangle has legs 6 and 8. Find the hypotenuse.
- Use a² + b² = c²: 6² + 8² = 36 + 64 = 100.
- c = √100 = 10.
- Shortcut: 6-8-10 is just the 3-4-5 triangle doubled. Recognizing triples saves time.
A circle has radius 6. Find the area of a 90° sector.
- Full circle area = πr² = π(6²) = 36π.
- A 90° sector is 90/360 = 1/4 of the circle.
- Sector area = (1/4)(36π) = 9π.
Two triangles are similar. The smaller has sides 3, 4, 5. The larger's shortest side is 9. Find its longest side.
- Find the scale factor using matching sides: 9 ÷ 3 = 3.
- Every side of the larger triangle is 3 times the smaller one.
- Longest side = 5 × 3 = 15.
Common mistakes to avoid
- Using the diameter when the formula calls for the radius (or vice versa). Circumference = 2πr, but also = πd — don't mix them.
- Forgetting the ½ in the triangle area formula: area = ½ × base × height.
- Matching the wrong pair of sides when finding a scale factor. Always pair shortest with shortest, longest with longest.
- Assuming a triangle is right-angled when the problem never says so. You can only use a² + b² = c² on right triangles.
265 questions, 98 distinct question types · you answer 12 at a time and can keep going for as long as you like.
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Frequently asked questions
What geometry and trig do I need for the SAT?
Expect angles and lines, triangle properties including similar and right triangles, circles with arcs and area, and area and volume of common shapes. Trigonometry covers the sine, cosine, and tangent ratios in right triangles. The Pythagorean theorem shows up often. You don't need advanced proofs; you need to recognize standard setups and apply the right relationship or formula accurately.
How do I remember trig ratios like sine and cosine?
Use SOH CAH TOA for right triangles: sine equals opposite over hypotenuse, cosine equals adjacent over hypotenuse, and tangent equals opposite over adjacent. Identify the angle you're working from, then label the sides as opposite, adjacent, and hypotenuse relative to it. Once the sides are labeled, plug into the right ratio. Practice on several triangles so the labeling becomes automatic under time pressure.
When do I use the Pythagorean theorem?
Use it in any right triangle when you know two sides and need the third. The theorem says the two legs squared and added equal the hypotenuse squared. Make sure the triangle has a right angle and that you've identified the hypotenuse, which is always opposite the right angle and the longest side. Recognizing hidden right triangles inside a figure often unlocks the problem.
Are geometry formulas given on the SAT?
The math section provides a reference sheet with common formulas, but you'll work much faster if you already know the essentials for area, circles, and the Pythagorean theorem. Relying on the sheet for every problem costs time. Memorize the frequently used formulas and understand when each applies, and treat the reference as a backup for the ones you use less often.