To determine the correct rule for triangle congruence in this diagram, let’s analyze the marked information:

1. Side Marks: Both triangles $\triangle CBF$ and $\triangle GBH$ have two pairs of congruent sides marked by single and double tick marks.
2. Angle Marks: Each triangle has a congruent angle marked with a red arc at $\angle CBF$ and $\angle GBH$.

Given these observations, we can apply the SAS (Side-Angle-Side) congruence rule. This rule states that if two sides and the included angle of one triangle are congruent to two sides and the included angle of another triangle, the triangles are congruent.

Therefore, the answer is SAS.

Would you like a detailed explanation of the SAS rule or its application?

Here are some related questions you might find helpful:

1. What are other congruence rules for triangles, like ASA, SSS, and AAS?
2. Can triangles be congruent without any angle or side markings?
3. How does the SAS rule differ from other congruence rules?
4. When is it impossible to prove triangle congruence?
5. How does triangle congruence relate to similarity?

Tip: Remember, for SAS to apply, the congruent angle must be between the two marked sides in each triangle.