In `triangle ABC and triangle DEF` , if `angle A = angle F, angle B = angle D ` and AB = FD , then which one of the folloing congruence conditions applies :

Options

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

Answer

To determine the congruence condition that applies to triangles ABC and DEF given the conditions, we can follow these steps:

### Step-by-Step Solution:

1. **Identify the Given Information:**
- We have two triangles: Triangle ABC and Triangle DEF.
- The angles and sides given are:
- \( \angle A = \angle F \)
- \( \angle B = \angle D \)
- \( AB = FD \)

2. **Analyze the Congruence Conditions:**
- We need to identify which congruence condition applies based on the given information. The common congruence conditions for triangles are:
- SSS (Side-Side-Side)
- SAS (Side-Angle-Side)
- ASA (Angle-Side-Angle)
- AAS (Angle-Angle-Side)
- RHS (Right angle-Hypotenuse-Side) for right triangles.

3. **Apply the Given Conditions:**
- From the information:
- We have two angles (\( \angle A \) and \( \angle B \)) that are equal to the corresponding angles in triangle DEF (\( \angle F \) and \( \angle D \)).
- We also have one side (\( AB \)) that is equal to the corresponding side (\( FD \)).
- This matches the ASA (Angle-Side-Angle) condition because we have:
- One angle (\( \angle A \))
- One side (\( AB \))
- Another angle (\( \angle B \))

4. **Conclusion:**
- Therefore, the congruence condition that applies to triangles ABC and DEF is ASA (Angle-Side-Angle).

### Final Answer:
The congruence condition that applies is **ASA (Angle-Side-Angle)**.

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