~15% of Math section · ~5–7 questions per test

Geometry & Trigonometry
Practice Questions

Geometry & Trigonometry questions cover area, volume, angle relationships, the Pythagorean theorem, and the basics of right-triangle trigonometry. A reference sheet with key formulas is provided during the test, but knowing when and how to apply each formula efficiently is the real skill being assessed.

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Explanations

About Geometry & Trigonometry

Geometry and Trigonometry make up roughly 15% of the Math section and are spread across both the no-calculator and calculator modules. The current test format is less focused on formal proof and more focused on applying formulas and relationships to find missing lengths, areas, and angle measures in real or described diagrams. The provided reference sheet lists major formulas, so memorization is less important than fluency in application.

The four core subtopics move from two-dimensional figures to three-dimensional solids, from basic angle arithmetic to the formal relationships in special triangles, and from the Pythagorean theorem to sine, cosine, and tangent. Many questions combine multiple concepts—for example, a circle problem that also requires the Pythagorean theorem to find a chord length, or a trigonometry problem that also tests similar triangle properties. Building a flexible toolkit rather than a rigid list of procedures is the key to handling these hybrid questions.

Right-triangle trigonometry has grown in prominence on the current test compared to earlier versions. You need to be comfortable setting up sinθ = opposite/hypotenuse, cosθ = adjacent/hypotenuse, and tanθ = opposite/adjacent, as well as recognizing complementary angle relationships: sin(θ) = cos(90° − θ). Circle questions frequently involve arc length, sector area, and the central vs. inscribed angle theorem. Knowing these rules cold—without having to look them up on the reference sheet every time—is what separates fast, confident test-takers from slow, uncertain ones.

What You'll Practice

Computing areas and perimeters of standard 2D shapes
Finding surface areas and volumes of 3D solids
Using angle relationships: supplementary, vertical, alternate interior, corresponding
Applying the Pythagorean theorem and recognizing Pythagorean triples
Setting up and solving right-triangle trigonometry (sin, cos, tan, and their complements)
Working with circle properties: central angles, inscribed angles, arc length, and sector area

Why Geometry & Trigonometry Matters for Your Score

Geometry is the visual branch of mathematics, and spatial reasoning skills tested here are directly relevant to architecture, engineering, design, and science. Even for students not pursuing STEM fields, the geometry domain rewards systematic, organized problem-solving—skills that transfer everywhere. On the test, strong geometry performance is achievable with relatively focused review, making it one of the higher-ROI areas to study.

Geometry & Trigonometry Subtopics

Each subtopic page has 8–10 practice questions, concept explanations, common mistakes, and strategy tips tailored to that specific skill.

Area and Volume

Questions asking you to compute or compare areas of 2D figures and surface areas and volumes of 3D solids.

Lines, Angles, and Triangles

Questions covering angle relationships formed by parallel lines, properties of triangles, congruence, similarity, and the triangle inequality.

Right Triangles and Trigonometry

Questions applying the Pythagorean theorem, SOH-CAH-TOA, and complementary angle trig identities to find side lengths and angle measures in right triangles.

Circles

Questions covering circle area, circumference, arc length, sector area, central and inscribed angles, and the equation of a circle in the coordinate plane.

Geometry Sample Questions

Strategy Tips for Geometry

TIP 1

Draw and label everything

Even when the test provides a figure, redraw key information directly onto it: label angle measures you calculate, mark equal sides or angles with tick marks, and write any intermediate lengths. The geometry questions that stump students most often do so because they try to hold too much in working memory instead of annotating the figure.

TIP 2

Use the reference sheet strategically, not habitually

The test provides a reference sheet with formulas for area, volume, and special triangles. Use it when you're uncertain, but try to know the most common formulas cold—area of a triangle, circle, rectangle—so you only need the sheet for less common items like the volume of a cone or sphere. Constant reference-sheet trips waste time.

TIP 3

For trig, always label sides relative to the angle

Before applying SOH-CAH-TOA, label which side is opposite, adjacent, and the hypotenuse relative to the specific angle mentioned in the problem. Students most often make mistakes when they label relative to the wrong angle. The hypotenuse is always the longest side, opposite the right angle—that label never changes. Opposite and adjacent, however, change depending on which acute angle you're working from.

TIP 4

Convert angles to arc length with the proportion

Arc length and sector area questions almost always yield to the same proportion: (central angle / 360°) = (arc length / circumference) = (sector area / total circle area). Write this proportion out explicitly, plug in two known values, and solve for the third. This single structure handles nearly every circle question on the test.

Frequently Asked Questions — Geometry

Does the test provide a geometry formula sheet?

Yes. A reference sheet with the most important formulas—including areas of triangles, circles, rectangles, and trapezoids, as well as volumes of rectangular prisms, cylinders, spheres, cones, and pyramids, plus the 30-60-90 and 45-45-90 special triangle ratios—is accessible during the Math section. You should still aim to know the most common formulas from memory so you spend less time looking them up.

How much trigonometry is on the test?

Trigonometry has grown on the current test format. You should be comfortable with right-triangle trig (SOH-CAH-TOA), the complementary angle identity (sin θ = cos(90° − θ)), and using the unit circle for basic angles. The Law of Sines and Law of Cosines are not tested. Arc length, sector area, and radian-degree conversion are tested as part of the Circles subtopic.

Will I see figures/diagrams, or are problems text-only?

Most geometry questions include a figure, though some describe the figure entirely in the problem text. Even when a figure is provided, it may not be drawn to scale—the problem will say 'Note: Figure not drawn to scale.' In those cases, don't rely on visual estimation; use only the labeled values and the relationships you know.

Are coordinate geometry questions in this domain?

Questions involving the coordinate plane—distance formula, midpoint, slope, equations of circles—appear primarily in the Algebra and Advanced Math domains, not in Geometry & Trigonometry. This domain focuses on Euclidean geometry, classical angle relationships, and trigonometry.

What are the most important things to review first?

Prioritize the Pythagorean theorem (and the 3-4-5, 5-12-13, and 8-15-17 triples), the area formulas for triangles and circles, the arc/sector proportion, and the three basic trig ratios. These appear on almost every test. 3D volume questions are less common but are straightforward if you know the formulas, so a quick review is high-ROI.

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Geometry & Trigonometry Practice Questions