Triangle Congruence Calculator
Determine if two triangles are congruent using SSS, SAS, ASA, and AAS methods
Compare Two Triangles
Triangle 1
Triangle 2
Congruence Analysis
Enter valid triangle data for both triangles to compare congruence
Example: SSS Congruence
Triangle 1 (SSS)
Sides: a = 3 cm, b = 4 cm, c = 5 cm
Type: Right triangle (3-4-5)
Triangle 2 (SSS)
Sides: a = 3 cm, b = 4 cm, c = 5 cm
Result: ✅ Congruent (SSS postulate)
Congruence Methods
Side-Side-Side
All three sides are congruent
Side-Angle-Side
Two sides and included angle are congruent
Angle-Side-Angle
Two angles and included side are congruent
Angle-Angle-Side
Two angles and a non-included side are congruent
Important Notes
Congruent triangles have identical shape AND size
Similar triangles have the same shape but different sizes
SSA (Side-Side-Angle) is NOT a valid congruence method
AAA only proves similarity, not congruence
Understanding Triangle Congruence
What is Congruence?
Two triangles are congruent if all corresponding sides and angles are equal. Congruent triangles have the same shape and size, meaning one can be transformed into the other through rotation, reflection, or translation without changing dimensions.
Congruence vs Similarity
- •Congruent: Same shape AND same size
- •Similar: Same shape but different sizes
- •Neither: Different shapes and possibly different sizes
Congruence Postulates
SSS Postulate
If three sides of one triangle are congruent to three sides of another triangle, then the triangles are congruent.
SAS Postulate
If two sides and the included angle of one triangle are congruent to two sides and the included angle of another triangle, then the triangles are congruent.
ASA Postulate
If two angles and the included side of one triangle are congruent to two angles and the included side of another triangle, then the triangles are congruent.
AAS Theorem
If two angles and a non-included side of one triangle are congruent to two angles and the corresponding non-included side of another triangle, then the triangles are congruent.