Two triangles are considered congruent when they are identical in shape and size, which means all corresponding sides and angles are equal. There are several conditions under which this congruence can be established:
- Side-Side-Side (SSS) Congruence: If all three sides of one triangle are equal to the three sides of another triangle, the triangles are congruent.
- Side-Angle-Side (SAS) Congruence: If two sides and the included angle of one triangle are equal to the corresponding two sides and angle of another triangle, then the triangles are congruent.
- Angle-Side-Angle (ASA) Congruence: If two angles and the side between them in one triangle are equal to two angles and the corresponding side in another triangle, the triangles are congruent.
- Angle-Angle-Side (AAS) Congruence: If two angles and a non-included side of one triangle are equal to two angles and the corresponding side of another triangle, the triangles are congruent.
- Hypotenuse-Leg (HL) Congruence (right triangles only): If the hypotenuse and one leg of a right triangle are equal to the hypotenuse and one leg of another right triangle, the triangles are congruent.
Using these conditions, one can reliably determine if two triangles are congruent. It’s essential in various applications in geometry to establish this relationship correctly.