Geometry Solver

The Geometry Solver takes a figure and a question and works out the missing quantity with a justified step for each move. Angle chasing with parallel lines and transversals. Triangle problems with the Pythagorean theorem, similarity, and congruence. Circle theorems: inscribed angles, chords, tangents, arcs. Area and perimeter of polygons and composite shapes. Surface area and volume of solids. Coordinate geometry: distance, midpoint, slope, equations of lines and circles. Two-column and paragraph proofs with the reason named at each statement. Transformations, reflections, rotations, translations, and dilations on the coordinate plane are computed point by point, and constructions are described as a sequence of compass-and-straightedge steps.

Photograph the diagram with the labels visible. That is the fastest input, since most geometry problems live in the picture. If there is no diagram, describe the figure: "triangle ABC with AB = 5, BC = 7, angle B = 60 degrees, find AC". State what you need: a length, an angle, an area, or a proof. Set Answer form to exact for radicals and pi, decimal for a rounded measurement. If the question refers to a figure by letters, list the vertices in order so the solver reads the shape the same way you do. State units when the answer needs them, and state whether an angle answer should be in degrees or radians.

Output: the requested value or the completed proof first. Then the chain: which theorem or definition applies, the equation it produces, and the arithmetic. Proofs come as numbered statements with reasons. The working is shown so you can check it. For a problem that is mostly trigonometric ratios, the Trigonometry Solver is tuned for it. For a figure defined by equations rather than lengths, the Function Analyzer and the Equation Solver handle the algebra. A follow-up can ask for an alternative proof, a different justification for one statement, or the same area computed by a second method as a check. Each theorem is named exactly as textbooks name it so it can be cited in your own work.