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Triangle Congruence by Side Lengths — result sheet
Compare two triangles by their three side lengths, test SSS congruence, and compare perimeter and area.
Inputs used
Results
Visual chart
Breakdown
Calculation steps
Returned data table
Formula and methodology
Formula: Sort each side set and compare corresponding values. Equal three-side sets establish SSS congruence; each area uses Heron's formula and each perimeter is the sum of the three sides.
This page answers the narrow side-only question: do two supplied side sets describe congruent triangles under the SSS criterion? Sorting makes the comparison independent of input order, while strict triangle checks prevent invalid side sets from being labeled congruent.
This result follows the calculator's declared inputs, precision, validation boundaries, and model limits.
Input contract
- Triangle 1 side a — length units; minimum 1.0E-6; maximum 1000000000
- Triangle 1 side b — length units; minimum 1.0E-6; maximum 1000000000
- Triangle 1 side c — length units; minimum 1.0E-6; maximum 1000000000
- Triangle 2 side a — length units; minimum 1.0E-6; maximum 1000000000
- Triangle 2 side b — length units; minimum 1.0E-6; maximum 1000000000
- Triangle 2 side c — length units; minimum 1.0E-6; maximum 1000000000
Worked example
| Input | Value |
|---|---|
| Triangle 1 side a | 3 |
| Triangle 1 side b | 4 |
| Triangle 1 side c | 5 |
| Triangle 2 side a | 5 |
| Triangle 2 side b | 3 |
| Triangle 2 side c | 4 |
Congruent by side lengths; both perimeters =12 and both areas =6 square units.
Assumptions and limits
- Each triangle is Euclidean and non-degenerate.
- Side lengths are positive and use one consistent unit within the comparison.
- SSS is used as the congruence criterion; no angle measurements are inferred.
- A small scale-aware tolerance is used for decimal measurement comparisons.
- Equal side sets establish congruence up to rigid motion and reflection, not a particular placement.
- Heron areas are computed from the supplied side lengths.
- The result does not assess measurement uncertainty beyond the numeric tolerance.
- For a full ASA, SAS, AAS, or right-triangle proof, provide the relevant angle information separately.
Calculator note
Source and methodology
Use the official WorldCalculate methodology policy for the source, formula, precision, and boundary standards behind this calculator.
Planning estimate, not financial, medical, legal, or professional advice. © WorldCalculate — reuse with attribution. Built and curated by Hassan ALRowaie.
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