To prove that two triangles are congruent, you can use several theorems, including:
- SSS (Side-Side-Side) Congruence Theorem: If the three sides of one triangle are equal to the three sides of another triangle, then the two triangles are congruent.
- SAS (Side-Angle-Side) Congruence 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 two triangles are congruent.
- ASA (Angle-Side-Angle) Congruence Theorem: If two angles and the side between them of one triangle are equal to two angles and the side between them of another triangle, then the two triangles are congruent.
- AAS (Angle-Angle-Side) Congruence Theorem: If two angles and a non-included side of one triangle are equal to two angles and the corresponding non-included side of another triangle, then the two triangles are congruent.
- HL (Hypotenuse-Leg) Congruence Theorem: This applies to right triangles. If the hypotenuse and one leg of one right triangle are equal to the hypotenuse and one leg of another right triangle, then the two triangles are congruent.
Choosing which theorem to use depends on the information provided about the triangles. Theorems like SSS and SAS are often the most commonly applied due to their straightforward nature in proving congruence.