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The question asks to identify the correct pair of congruent triangles under the **RHS (Right-angle-Hypotenuse-Side)** congruence rule. Let's break down the given figure:

- **Triangles Involved**: There are several triangles in the diagram, including \( \triangle AFC \), \( \triangle AEB \), \( \triangle BEC \), \( \triangle CFB \), and others.
  
- **RHS Rule**: This rule applies when two triangles each have:
  1. A right angle (both triangles must have a right angle).
  2. Equal hypotenuses.
  3. One equal side adjacent to the right angle.

### Observations:

1. **Right angles**: There are right angles at points \( E \) and \( F \) (since \( \angle AEC = 90^\circ \) and \( \angle AFB = 90^\circ \)).
   
2. **Hypotenuses**: The hypotenuses of the triangles involved would be \( AC \) and \( AB \), respectively.

3. **Equal sides**: The segments \( AE = AF \) (as shown by the equal marks), indicating that the sides adjacent to the right angles in \( \triangle AFC \) and \( \triangle AEB \) are equal.

Given these observations, the pair of triangles that satisfy the RHS congruence rule is:

\[
\boxed{\triangle AFC \cong \triangle AEB}
\]

This is the correct answer because both triangles have:
- Right angles at \( E \) and \( F \),
- Equal hypotenuses \( AC \) and \( AB \),
- And the sides \( AE = AF \).

Would you like further details or have any questions?

### Related Questions:
1. How does the RHS rule differ from other congruence rules like SAS or SSS?
2. Why is the hypotenuse important in proving triangle congruence under the RHS rule?
3. What is the significance of right angles in triangle congruence?
4. How can you use the congruence of triangles to solve for unknown side lengths?
5. Can the RHS rule be applied to non-right triangles?

**Tip**: Always verify the three criteria of the RHS rule (Right Angle, Hypotenuse, and Side) before concluding congruence.

The teacher has drawn a figure on the board as shown below and given four statements. She asked students to identify the correct statement under the RHS congruence rule.

Learn how to identify congruent triangles using the RHS (Right-angle-Hypotenuse-Side) rule. This problem involves analyzing a geometric diagram with right angles, equal hypotenuses, and equal sides. Suitable for students in Grades 7-9.

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