Congruent Triangles Calculator

Work out congruent triangles instantly with clear inputs, formula shown and shareable results.

About Congruent Triangles Calculator

Two triangles are congruent when all three pairs of corresponding sides are equal (SSS), which forces the angles to match as well. If the sides are in a constant ratio other than 1, the triangles are similar rather than congruent.

Formula

SSS congruence

a₁ = a₂, b₁ = b₂, c₁ = c₂ (after sorting) ⇒ congruent

Worked example

With the default values below, Congruent Triangles Calculator returns Result of Congruent by SSS. Change any input above and every figure here is recalculated in your browser.

Inputs used

Triangle 1 sides (comma separated): 5, 7, 9
Triangle 2 sides (comma separated): 9, 5, 7

Results

Result: Congruent by SSS
Perimeter of triangle 1: 21.0000
Perimeter of triangle 2: 21.0000
Area of triangle 1: 17.4123

Step by step

1Values used
2SSS congruence
3Result= Congruent by SSS
4Perimeter of triangle 1= 21.0000
5Perimeter of triangle 2= 21.0000
6Area of triangle 1= 17.4123

Assumptions and limits

The result is derived only from the 2 inputs listed above. Anything not among them is not part of the calculation.
In particular, this calculator does not take inflation, tax, fees or charges or compounding frequency into account.
Figures are rounded for display to 4 decimal places, so totals built from several rounded parts can differ slightly from the unrounded arithmetic.

How these calculators are built and tested is described on the Methodology page. If a figure looks wrong, please report it.

Frequently Asked Questions

Does the order I type the sides matter?

No. The sides are sorted before comparison, so any ordering of the same three lengths is recognised.

Is SSA a valid congruence test?

No. Side-side-angle is ambiguous and can describe two different triangles, which is why it is excluded.