Two shapes are congruent if they are identical in size and shape — one can be mapped onto the other by a combination of rotations, reflections, and translations (but not enlargements).
Congruence criteria for triangles — to prove two triangles are congruent, show one of:
- SSS — all three sides are equal
- SAS — two sides and the included angle are equal
- ASA (or AAS) — two angles and a corresponding side are equal
- RHS — right angle, hypotenuse, and one other side are equal
When writing a congruence proof, state which criterion you are using and show each piece of evidence clearly with a reason (e.g. "common side", "alternate angles", "given").
Congruence vs similarity: congruent shapes are identical in size; similar shapes have the same angles but different sizes (linked by a scale factor).
Common error: claiming SAS when the angle is not between the two given sides — the angle must be enclosed by the two sides.