Enter Triangle Measurements
Use corresponding sides and angles from both triangles. Provide enough values for SSS, SAS, ASA, AAS, or RHS checking.
Plotly Comparison Graph
The chart compares corresponding sides and angles for both triangles. Submit values to update the visual comparison.
Example Data Table
This example shows two congruent triangles that match by SSS and also align with valid angle totals.
| Example | Triangle A | Triangle B | Expected Result |
|---|---|---|---|
| Sides | a = 5, b = 6, c = 7 | a = 5, b = 6, c = 7 | Congruent by SSS |
| Angles | A = 48.19°, B = 58.41°, C = 73.40° | A = 48.19°, B = 58.41°, C = 73.40° | Angle sum valid |
| Tolerances | 1% side, 0.5° angle | 1% side, 0.5° angle | Stable comparison |
Formula Used
Triangle congruence means two triangles have equal corresponding sides and equal corresponding angles, so one triangle fits exactly over the other.
Core Rules
SSS: If all three corresponding sides are equal, the triangles are congruent.
SAS: If two corresponding sides and the included angle are equal, the triangles are congruent.
ASA: If two corresponding angles and the included side are equal, the triangles are congruent.
AAS: If two corresponding angles and a non-included side are equal, the triangles are congruent.
RHS: For right triangles, equal hypotenuse and one corresponding side prove congruence.
Validation Checks
Triangle inequality: a + b > c, a + c > b, b + c > a
Angle sum rule: A + B + C = 180°
Side tolerance test: |x − y| ≤ max(|x|, |y|, 1) × tolerance%
Angle tolerance test: |θ₁ − θ₂| ≤ angle tolerance
How to Use This Calculator
- Enter the available side and angle measurements for Triangle A.
- Enter the corresponding measurements for Triangle B.
- Choose side and angle tolerance values for practical comparison.
- Press Check Congruence to evaluate the triangles.
- Read the result summary shown above the form.
- Review the matched criteria table and the comparison graph.
- Download the result data as CSV or PDF if needed.
Frequently Asked Questions
1) What does congruent mean in triangles?
Congruent triangles have the same shape and the same size. Their corresponding sides and angles match, so one triangle can be placed exactly on top of the other.
2) Which congruence rules does this checker support?
This checker supports SSS, SAS, ASA, AAS, and RHS. It also validates triangle inequality and angle sums before giving a final interpretation.
3) Why do I need corresponding measurements?
Congruence depends on comparing matching parts. Side a in one triangle should match side a in the other, and the same idea applies to the angles.
4) What is the purpose of tolerance values?
Tolerances help when measurements come from rounding, drawing tools, or experiments. Small differences can still be treated as matches within the accepted margin.
5) Can the checker work with partial information?
Yes. You do not always need every measurement. You only need enough consistent information to verify at least one valid congruence rule.
6) Why might I see an input warning?
Warnings appear when side lengths break triangle inequality or when the entered angles do not total 180 degrees within the chosen tolerance.
7) Is AAA enough to prove congruence?
No. AAA only proves similarity, not congruence. Triangles can have the same angles but different sizes, so more information is needed.
8) When is RHS useful?
RHS is useful only for right triangles. If both triangles contain a right angle, then matching the hypotenuse and one corresponding side proves congruence.