Congruent Triangles Calculator

Enter the known sides and angles of two triangles and select a congruence criterion (SSS, SAS, ASA, or AAS) to test whether they are congruent. Choose your criterion, fill in the corresponding side lengths (a, b, c) and angles (α, β, γ) for each triangle, and the calculator tells you whether the triangles are congruent, which rule confirms it, and shows a breakdown of the compared values.

Select the rule that matches the known measurements of both triangles.

units
units
units
°
°
°
units
units
units
°
°
°

Values within this tolerance are treated as equal. Default 0.001 handles floating-point rounding.

Results

Congruence Result

--

Criterion Applied

--

Matching Values

--

Triangle 1 Summary

--

Triangle 2 Summary

--

Side & Angle Comparison: Triangle 1 vs Triangle 2

Results Table

Frequently Asked Questions

What does congruent mean in geometry?

Congruent means 'identical in form' — two shapes are congruent if they have exactly the same size and shape. For triangles, this means all three corresponding sides and all three corresponding angles are equal. You can think of it as two triangles that would perfectly overlap if one were placed on top of the other.

What are the four main triangle congruence criteria?

The four accepted criteria are SSS (all three sides equal), SAS (two sides and the included angle equal), ASA (two angles and the included side equal), and AAS (two angles and a non-included adjacent side equal). Each criterion provides exactly enough information to uniquely determine a triangle's shape and size.

Are AAA triangles always congruent?

No — AAA (three equal angles) proves that two triangles are similar in shape, but not necessarily congruent in size. Two triangles can have the same three angles but different side lengths, making them scaled versions of each other. To confirm congruence you always need at least one pair of equal sides.

Is SSA enough to prove two triangles are congruent?

No, SSA (two sides and a non-included angle) is not a valid congruence criterion. It is sometimes called the 'ambiguous case' because the same SSA values can produce two different triangles or even no valid triangle at all. This is why only SSS, SAS, ASA, and AAS are accepted as proof of congruence.

Is SAA the same as AAS?

Yes, SAA and AAS refer to the same configuration — two angles and a side that is not between them. Because the three angles of a triangle always sum to 180°, knowing two angles automatically determines the third, which effectively means AAS also determines the triangle's shape and size uniquely.

What is the difference between congruent and similar triangles?

Congruent triangles are identical in both shape and size — all sides and angles match exactly. Similar triangles share the same shape (equal angles) but can be different sizes, meaning their sides are proportional rather than equal. Congruence is a stricter condition than similarity.

How do I use this congruent triangles calculator?

Select the congruence criterion that matches the information you have (SSS, SAS, ASA, or AAS), then enter the corresponding side lengths and angles for both Triangle 1 and Triangle 2. The calculator compares the relevant values and tells you whether the triangles are congruent under the chosen rule, along with a full side-by-side breakdown table.

Can a triangle have sides that violate the triangle inequality?

No — for any triangle to be valid, the sum of any two side lengths must be greater than the third side. This is called the triangle inequality theorem. If you enter side values that violate this rule, the calculator will flag the input as an invalid triangle rather than returning a congruence result.

More Math Tools