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Mathematics
Congruent triangles — Which measurements are enough?
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Keep sides or angles equal, drag the trial triangle and overlay it on the reference triangle.
ABC · Reference triangleA′B′C′ · Trial triangle
Drag C′ to change the triangle
A′B′ = AB = 6 cm
A′C′ = AC = 4 cm
Each constraint matches triangle ABC.
Drag C′ to change the triangle
Insufficient data
Two sides
Two sides stay fixed, but their included angle can change. The third side can therefore differ.
Congruent — can coincide
This pair is congruent, but the given data do not guarantee it. Try dragging.
Largest side difference 0 cm
| Side / Angle | ABC | A′B′C′ |
|---|---|---|
| AB | 6 cm | 6 cm |
| AC | 4 cm | 4 cm |
| BC | ≈ 5.29 cm | ≈ 5.29 cm |
| ∠A | 60° | 60° |
| ∠B | ≈ 40.9° | ≈ 40.9° |
| ∠C | ≈ 79.1° | ≈ 79.1° |
≈ marks rounded values. A constraint denotes exact equality in the model.
Model notes
- The model uses non-degenerate plane triangles with A–A′, B–B′ and C–C′ as corresponding vertices. Displayed measurements may be rounded.
- Overlaying only translates, rotates or reflects; it never scales one triangle. Viewport zoom affects both drawings equally.
- The angle range 20°–140° and base range 3–9 cm keep the drawing readable. These limits are not conditions of the theorems.
- Dragging illustrates relationships and finds counterexamples; it does not replace proof. This resource covers three basic criteria, not every set of measurements or special right-triangle criteria.