Which one of the following is not a criterion for congruence of two triangles?

Options

A. ASA
B. SSA
C. SAS
D. SSS

Answer

To determine which of the given options is not a criterion for the congruence of two triangles, we will analyze each option step by step.

### Step-by-Step Solution

1. **Understand the Criteria for Congruence**: Congruence of triangles means that two triangles are identical in shape and size. There are specific criteria that help us determine if two triangles are congruent.

2. **Evaluate Option 1: ASA (Angle-Side-Angle)**:
- ASA states that if two angles and the included side of one triangle are equal to two angles and the included side of another triangle, then the two triangles are congruent.
- **Conclusion**: ASA is a valid criterion for congruence.

3. **Evaluate Option 2: SSA (Side-Side-Angle)**:
- SSA states that if two sides and a non-included angle of one triangle are equal to two sides and the corresponding non-included angle of another triangle, it does not guarantee that the triangles are congruent.
- **Conclusion**: SSA is NOT a valid criterion for congruence.

4. **Evaluate Option 3: SAS (Side-Angle-Side)**:
- SAS states that 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.
- **Conclusion**: SAS is a valid criterion for congruence.

5. **Evaluate Option 4: SSS (Side-Side-Side)**:
- SSS states that if all three sides of one triangle are equal to all three sides of another triangle, then the two triangles are congruent.
- **Conclusion**: SSS is a valid criterion for congruence.

6. **Final Conclusion**: Among the options provided, SSA is the only one that is not a criterion for congruence of triangles.

### Answer
The option that is not a criterion for congruence of two triangles is **Option 2: SSA (Side-Side-Angle)**.

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