Practice circles, triangles, trigonometric ratios, radians, area, volume, similarity, and geometric transformations with free SAT-style questions and instant results.
SAT geometry problems often hide a simple relationship inside a diagram, a word problem, or a coordinate system. These practice tests help you recognize the structure before reaching for a formula — whether the problem involves a triangle, a circle, trigonometry, three-dimensional measurement, or a geometric transformation.
Each test concentrates on a different geometric structure, so you can practice recognizing which relationships are useful before you begin calculating.
Work with parallel lines, transversals, vertical and supplementary angles, triangle angle relationships, exterior angles, triangle inequality, and geometric reasoning that connects several facts in the same figure.
Practice sine, cosine, tangent, the Pythagorean theorem, special right triangles, angle relationships, and converting between degrees and radians when a problem combines geometry with trigonometric information.
Connect the geometry of circles with coordinate algebra. Practice center and radius, circle equations, arcs, sectors, central and inscribed angles, tangent relationships, and completing the square.
Move between two- and three-dimensional measurement. Practice area, circumference, surface area, and volume while paying attention to units, dimensions, scale changes, and the information actually needed by the problem.
Decide what stays the same and what changes when figures are compared or transformed. Practice scale factor, corresponding sides and angles, congruence, similarity, translations, rotations, reflections, and dilations in the coordinate plane.
A diagram is rarely decoration. Marks, equal lengths, parallel lines, right-angle symbols, coordinates, and labels can tell you which theorem or formula connects the unknown quantity to what you already know.
Separate stated measurements and relationships from details you are only assuming from the appearance of the drawing.
Decide whether the useful structure is a right triangle, similar figures, a circle, parallel lines, or a three-dimensional solid.
Choose a theorem, proportion, trigonometric ratio, or measurement formula that contains both.
An angle, length, area, or volume should be reasonable for the figure and expressed in the correct type of unit.
First determine the relationship in the figure. A formula is useful only after you know what its variables represent. This is especially important when a SAT problem includes extra measurements that are not needed for the final answer.
A few ideas are responsible for a large share of mistakes in SAT geometry and trigonometry problems.
You should rely on the measurements, labels, angle marks, and relationships stated in the problem rather than estimating a value from how the drawing looks. Use the diagram to organize information, not to replace mathematical reasoning.
In a right triangle, identify the sides relative to the angle you are using. Sine connects opposite and hypotenuse, cosine connects adjacent and hypotenuse, and tangent connects opposite and adjacent.
Look first for equal angles. Parallel lines, vertical angles, and a shared angle often create the angle relationships needed to establish similarity. Once triangles are similar, corresponding side lengths are proportional.
A 45-45-90 triangle has side ratios 1 : 1 : √2. A 30-60-90 triangle has side ratios 1 : √3 : 2, with the shortest side opposite the 30-degree angle.
A circle with center (h, k) and radius r has the form (x − h)² + (y − k)² = r². If the equation is expanded, completing the square can reveal the center and radius.
Lengths scale directly, areas scale by the square of the scale factor, and volumes scale by the cube. Applying the linear scale factor directly to an area or volume is a common error.
Congruent figures have the same size and shape. Similar figures have the same shape and equal corresponding angles, but their corresponding lengths may differ by a common scale factor.
Identify the first incorrect step. Check whether you misread the diagram, chose the wrong relationship, matched corresponding sides incorrectly, used the wrong formula, or made an algebraic calculation error. That tells you what skill actually needs practice.