Quick guide
How to use this calculator
- Choose the data pattern or theorem mode when the calculator offers one.
- Enter only the side lengths, angles, ratios, or coordinates labelled by the active mode.
- Read the main result first, then inspect the validated companion measurements and theorem check.
Calculation method
Apply the selected triangle relationship
Congruence is established when every corresponding measure required by the selected theorem matches.
The engine rejects degenerate triangles, impossible angle sums, failed strict inequalities, undefined ratios, and inconsistent theorem data before returning a result.
Worked example
Worked example
Two triangles with corresponding sides 3, 4, and 5 are congruent by SSS.
Congruence is established when every corresponding measure required by the selected theorem matches.
Supported inputs
Precision and limits
Units
Use one consistent length unit. Areas are reported in the square of that unit; angles are in degrees; coordinate tools use the entered Cartesian coordinate system.
Numeric range
Nonzero entered magnitudes must lie from 1e-50 through 1e50. Integer generators and exploratory modes also disclose tighter per-field limits.
Geometry
Ordinary triangle pages require a non-degenerate Euclidean triangle. The strict triangle inequalities and an interior-angle sum of 180° govern accepted data. Coordinate pages also reject vertex triples whose cross product is indistinguishable from zero at double-precision scale.
Precision
Calculations use finite double-precision arithmetic and normally display 12 significant digits. Coordinate-center tools also report offsets from vertex A; use those offsets when a very large coordinate translation rounds distinct absolute centers to the same displayed coordinate. The Pythagorean page retains a simple exact integer radical when the squared data make that representation available.
Calculator-specific rule
AAA is not a congruence criterion because it establishes only similarity.