Congruent Triangles Calculator
Check if two triangles are congruent using SSS, SAS, ASA, AAS, or HL
Triangle 1
Triangle 2
Triangle Congruence Postulates
SSS (Side-Side-Side)
If three sides of one triangle are equal to three sides of another triangle, the triangles are congruent.
SAS (Side-Angle-Side)
If two sides and the included angle are equal, the triangles are congruent.
ASA (Angle-Side-Angle)
If two angles and the included side are equal, the triangles are congruent.
AAS (Angle-Angle-Side)
If two angles and a non-included side are equal, the triangles are congruent.
HL (Hypotenuse-Leg)
For right triangles only: If the hypotenuse and one leg are equal, the triangles are congruent.
What Doesn't Work
- AAA (Angle-Angle-Angle): Only proves similarity, not congruence. Triangles could be different sizes.
- SSA (Side-Side-Angle): The ambiguous case - can produce 0, 1, or 2 triangles.
Frequently Asked Questions
What does congruent mean?
Congruent means exactly equal in shape and size. Congruent triangles have all corresponding sides equal and all corresponding angles equal.
What is CPCTC?
CPCTC stands for "Corresponding Parts of Congruent Triangles are Congruent." Once you prove triangles congruent, all corresponding parts are equal.
Why doesn't AAA prove congruence?
AAA only proves the triangles have the same shape (similar), but they could be different sizes. You need at least one side to determine size.
Why doesn't SSA work?
SSA is ambiguous because there can be 0, 1, or 2 triangles with the same SSA measurements. It doesn't uniquely determine a triangle.
When do I use HL?
HL only works for right triangles. It's a shortcut because the right angle is already known, so you only need hypotenuse and one leg.
What's the difference between congruent and similar?
Congruent = same shape AND same size. Similar = same shape but possibly different sizes. Congruent triangles are similar with scale factor 1.