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

Options

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

Answer

To determine which of the following is not a criterion for congruence of triangles, we first need to understand the established criteria for triangle congruence. The criteria are as follows:

1. **SSS (Side-Side-Side)**: If three sides of one triangle are equal to three sides of another triangle, then the two triangles are congruent.
2. **SAS (Side-Angle-Side)**: 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.
3. **ASA (Angle-Side-Angle)**: If two angles and the included side of one triangle are equal to two angles and the included side of another triangle, then the triangles are congruent.
4. **AAS (Angle-Angle-Side)**: If two angles and a non-included side of one triangle are equal to two angles and a non-included side of another triangle, then the triangles are congruent.
5. **RHS (Right Angle-Hypotenuse-Side)**: If the hypotenuse and one side of a right triangle are equal to the hypotenuse and one side of another right triangle, then the triangles are congruent.

Now, let's analyze the options given in the question:

- **SS (Side-Side)**: This criterion states that only two sides are equal, without any angle included. This is not a valid criterion for triangle congruence.

Since the question asks for which option is not a criterion for congruence of triangles, we can conclude:

**Answer**: The option that is not a criterion for congruence of triangles is **SS (Side-Side)**.