To prove that two triangles are congruent, one of the following theorems can be applied:
- Side-Side-Side (SSS) Congruence Theorem: This theorem states that if three sides of one triangle are equal in length to three sides of another triangle, then the two triangles are congruent.
- Side-Angle-Side (SAS) Congruence Theorem: According to this theorem, if two sides and the included angle of one triangle are equal to two sides and the included angle of another triangle, then the triangles are congruent.
- Angle-Side-Angle (ASA) Congruence Theorem: This states that if two angles and the side between them in one triangle are equal to two angles and the side between them in another triangle, the triangles are congruent.
- Angle-Angle-Side (AAS) Congruence Theorem: If two angles and a non-included side of one triangle are equal to two angles and a corresponding non-included side of another triangle, then the two triangles are congruent.
- Hypotenuse-Leg (HL) Theorem: In right triangles, if the hypotenuse and one leg of one triangle are equal to the hypotenuse and one leg of another triangle, then the two triangles are congruent.
Choosing the correct theorem depends on the information available about the triangles in question. By applying these theorems effectively, one can establish the congruence of two triangles, thus confirming that they are identical in shape and size.