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Triangle congruence is a fundamental concept in geometry, indicating that two triangles are identical in size and shape. This text delves into the Side-Side-Side (SSS) and Side-Angle-Side (SAS) congruence criteria, which are methods for proving triangle congruence. The SSS theorem requires three pairs of congruent sides, while the SAS theorem involves two congruent sides and the included angle. These principles are crucial for geometric proofs and have practical applications in various fields.

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## Definition of Triangle Congruence

### Essential Concept in Geometry

Triangle congruence signifies that two triangles have the same size and shape, regardless of their orientation

### Importance in Geometry and Practical Applications

Triangle congruence is pivotal in geometric proofs and practical applications

### Theorems for Determining Triangle Congruence

Mathematicians have formulated several theorems, including the SSS and SAS criteria, for efficiently determining triangle congruence

## SSS Criterion

### Definition and Explanation

The SSS criterion states that if the three pairs of corresponding sides of two triangles are congruent, then the triangles themselves are congruent

### Applicability

The SSS criterion can be applied to determine congruence even when triangles are oriented differently, as long as the corresponding sides are matched correctly

### Example

Two equilateral triangles with sides of identical length are congruent by the SSS criterion

## SAS Criterion

### Definition and Explanation

The SAS criterion states that if two triangles have two sides of the same length and the included angle is also congruent, then the triangles are congruent

### Applicability

The SAS criterion can be applied regardless of the triangles' orientation, as long as the corresponding sides and included angle are congruent

### Example

Two triangles with a 60-degree angle and two sides of length 6 cm forming that angle are congruent by the SAS criterion

## Comparison of SSS and SAS Criteria

### Differences

The SSS criterion compares all three sides of the triangles, while the SAS criterion involves two sides and the included angle

### Appropriate Use

The choice of criterion depends on the information available about the triangles

### Importance

Mastery of the SSS and SAS criteria is essential for students and professionals dealing with geometric figures

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