Free AI Geometry Solver

Geometry combines visual reasoning with algebraic calculation in ways that many students find challenging. Our free AI geometry solver interprets diagrams, applies theorems, and produces complete step-by-step solutions for every type of geometry problem you encounter in US high school and college courses.

Triangle Geometry

Triangles are the most heavily tested shape in geometry courses. The AI solver handles triangle congruence proofs using SSS, SAS, ASA, AAS, and HL criteria. It applies the Pythagorean theorem and its converse, calculates areas using multiple formulas (base-height, Heron's formula, coordinate method), and solves problems involving similar triangles and proportional reasoning.

For right triangles, the solver applies trigonometric ratios (sine, cosine, tangent) and their inverses to find missing sides and angles. It handles special right triangles (30-60-90 and 45-45-90) and applies the Law of Sines and Law of Cosines for non-right triangles.

Circle Geometry

Circle problems require knowledge of many specific theorems about chords, tangents, secants, arcs, and inscribed angles. The AI applies the inscribed angle theorem, central angle theorem, tangent-radius perpendicularity, chord-chord power of a point, and secant-tangent relationships. It calculates arc lengths, sector areas, and segment areas with clear formula application.

Equation of a circle problems in both standard and general form are solved with conversion steps shown. The solver identifies center and radius from any form and handles problems involving tangent lines to circles.

Geometric Proofs

Two-column proofs are one of the most difficult topics for geometry students. The AI solver constructs proofs by identifying given information, determining what needs to be proved, selecting appropriate theorems and postulates, and organizing the reasoning into a logical sequence. Each statement is paired with a justification.

The solver handles proofs involving parallel lines and transversals, triangle congruence and similarity, quadrilateral properties, and circle theorems. It can also construct paragraph proofs and coordinate geometry proofs when those formats are required.

Quadrilaterals and Polygons

Properties of parallelograms, rectangles, rhombi, squares, trapezoids, and kites are applied to solve for missing measurements and prove relationships. The solver also handles regular polygon problems including interior and exterior angle sums, apothem calculations, and area formulas.

Coordinate Geometry

The solver calculates distances, midpoints, slopes, and equations of lines in coordinate geometry problems. It proves geometric properties using coordinates, finds areas of polygons using the shoelace formula, and determines whether points are collinear. Transformation problems including translations, reflections, rotations, and dilations are solved with coordinate rules clearly stated.

Surface Area and Volume

Three-dimensional geometry problems involving prisms, cylinders, pyramids, cones, and spheres are solved with surface area and volume formulas applied step by step. Composite solid problems that combine multiple shapes are broken down into individual components. Cross-section analysis and solid of revolution problems bridge geometry with calculus.

Geometry builds spatial reasoning skills that are essential for physics, engineering, and architecture. Use our AI math solver to master these concepts at your own pace.