SAT Geometry and Trigonometry Study Guide
Prepare for SAT Math. Study angles, triangles, circles, coordinate geometry, trigonometry, area and volume. Choose a lesson below, or try mixed practice to check your skills.
All lessons
6 lessons
About this guide
Six complete lessons, 90 worked examples, and 24 mixed-practice questions.
How to use this guide
The goal is not to memorize a catalog of shapes. It is to recognize a small set of relationships inside unfamiliar figures. A difficult problem often becomes manageable after one useful construction: a radius to a tangent point, an altitude in a triangle, or a corresponding pair of sides in similar figures.
This guide develops the six Geometry and Trigonometry sections from the larger SAT Math outline. Every section contains explanations, original diagrams, and exactly 15 fully worked examples, for 90 in total. A separate 24-question mixed practice set lets you test whether you can choose a method without a chapter heading giving it away.
A productive study cycle
Learn. Read the concept lesson and reproduce its diagrams on scratch paper. State the conditions of each formula aloud: the Pythagorean theorem requires a right triangle; s
Attempt. Leave each worked solution closed. Identify the target and write a first equation before reading further. If stuck, open the solution and read only the “Recognize the structure” line, then try again.
Explain. After checking, write one sentence explaining why the method works. A correct answer with an unjustified assumption is not yet mastery.
Retrieve and transfer. Re-solve missed examples after a gap, then complete the mixed practice without looking back. Change one number or one condition and predict how the answer changes.
What the difficulty labels mean
Foundation isolates an essential skill. Standard connects a few ideas or representations. Challenge adds hidden structure, parameters, or a less obvious target. These are instructional labels, not official College Board difficulty ratings or score predictions. Some examples ask for more explanation than a test question so that the underlying reasoning is visible.
Before you begin
You should be comfortable solving linear equations, manipulating fractions and radicals, and substituting into formulas. Section 5 explains completing the square as it applies to circles. When a quadratic appears, the solution shows the required factoring or discriminant reasoning.
Unless stated otherwise, lengths are positive, angles in a triangle are interior angles, and figures are nondegenerate. In this guide, instructional sketches are schematic; use the stated relationships rather than measuring a picture. A square corner marker indicates a right angle, matching tick marks indicate equal lengths, and matching arrow marks indicate parallel lines.
Scope and notation
College Board groups this domain into measurement, lines/angles/triangles, right-triangle trigonometry, and circles.[1] The Math overview lists 5–7 Geometry and Trigonometry questions.[2] The full Math section has 44 questions in two 35-minute modules.[3]
The published framework also explicitly includes surface area, similarity, radians, unit-circle ratios, and circle equations.[4] Those topics are included here rather than relegated to optional enrichment. Coordinate geometry receives its own section because it connects geometric reasoning to algebra.
Section | Central question |
|---|---|
1. Lines and angles | Which angles must be equal, complementary, or supplementary? |
2. Triangles, congruence, and similarity | Which parts correspond, and what stays the same under scaling? |
3. Right triangles and trigonometry | Which side ratio or right-triangle relationship reaches the target? |
4. Circles and angle measure | How do the radius, angle, arc, and area relate? |
5. Coordinate geometry | What does an equation reveal about a figure, and vice versa? |
6. Perimeter, area, and volume | What is being measured, and how many dimensions are involved? |
Calculator use without calculator dependence
Bluebook includes Desmos scientific and graphing options; calculators may be used throughout Math. College Board’s current policy prohibits handheld calculators with computer algebra system (CAS) functionality. Check the official policy again before test day.[5]
Use a calculator for arithmetic, non-special trigonometric values, and numerical checks. Use algebra when the goal is an exact radical, a coefficient, or a general relationship. A graph can confirm an intersection, but it does not establish an exact value by appearance alone. Specific calculator tips appear where they improve a solution.
Answer forms and notation
In explanations, keep π, fractions, and radicals exact until the final step. A question asking for k when an area is kπ wants the coefficient, not the full area. Units belong in your reasoning even when the answer field only accepts a number.
The published student-produced-response directions allow fractions or decimals, not mixed-number notation, and specify how to fit repeating decimals in the entry field.[4] Follow the directions displayed in your test. This guide uses exact symbolic answers when they make the mathematics clearer; practice questions labeled student-produced response have numeric answers suitable for entry.
Your four-part check
Target: Did I answer the quantity requested? Conditions: Did I use only guaranteed relationships? Magnitude: Is the size plausible? Units: Should the answer be a length, an area, a volume, an angle, or a ratio?