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Triangle congruence is fundamental in geometry, involving criteria like SSS, SAS, ASA, AAS, and the HL theorem for right triangles. These theorems determine when two triangles are identical in shape and size, using the relationships between their sides and angles. Understanding these principles is crucial for solving geometric problems and proving congruence with limited information.

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## Definition of Triangle Congruence

### Triangle congruence is the concept of two triangles being identical in shape and size

## Criteria for Proving Triangle Congruence

### Side-Side-Side (SSS) Theorem

The SSS theorem states that if all three sides of two triangles are congruent, then the triangles are congruent

### Side-Angle-Side (SAS) Theorem

The SAS theorem states that if two sides and the included angle of two triangles are congruent, then the triangles are congruent

### Angle-Side-Angle (ASA) Theorem

The ASA theorem states that if two angles and the included side of two triangles are congruent, then the triangles are congruent

### Angle-Angle-Side (AAS) Theorem

The AAS theorem states that if two angles and a non-included side of two triangles are congruent, then the triangles are congruent

## Practical Applications of Triangle Congruence Theorems

### Triangle congruence theorems are useful tools for solving geometric problems and determining congruence with limited information about the triangles' sides and angles

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