It is given that `Delta ABC cong Delta FDE` and AB= 5 cm , `angle B=40^(@) " and " angle A= 80^(@)` then which of the following is true ?

Options

A. `DF=5 cm,angle F = 60^(@)`
B. `DF=5 cm,angle E = 60^(@)`
C. `DE=5 cm,angle E = 60^(@)`
D. `DE = 5 cm,angle D = 60^(@)`

Explanation

To solve the problem, we need to analyze the given information about the triangles and their properties.

### Step-by-Step Solution:

1. **Identify the Given Information:**
- We have two triangles: Triangle ABC and Triangle FDE.
- It is given that Triangle ABC is congruent to Triangle FDE (ΔABC ≅ ΔFDE).
- The lengths and angles of Triangle ABC are:
- AB = 5 cm
- Angle B = 40°
- Angle A = 80°

2. **Determine Angle C:**
- In any triangle, the sum of the interior angles is 180°.
- Therefore, we can find Angle C using the formula:
\[ \text{Angle C} = 180° - (\text{Angle A} + \text{Angle B}) = 180° - (80° + 40°) = 180° - 120° = 60° \]
- Thus, Angle C = 60°.

3. **Use Congruence to Find Corresponding Parts:**
- Since the triangles are congruent, the corresponding sides and angles are equal.
- Therefore, we can conclude:
- DE = AB = 5 cm (since AB corresponds to DE)
- Angle D = Angle A = 80° (since Angle A corresponds to Angle D)
- Angle E = Angle B = 40° (since Angle B corresponds to Angle E)
- Angle F = Angle C = 60° (since Angle C corresponds to Angle F)

4. **Summarize the Corresponding Parts:**
- From the congruence, we have:
- DE = 5 cm
- Angle D = 80°
- Angle E = 40°
- Angle F = 60°

5. **Check the Options:**
- Based on the analysis, we can check the options provided in the question:
- **Option A:** DE = 5 cm, Angle D = 80°, Angle F = 60° (This is correct)
- **Option B:** DE = 5 cm, Angle E = 60° (This is incorrect, Angle E = 40°)
- **Option C:** DE = 5 cm, Angle E = 40° (This is correct)
- **Option D:** DE = 5 cm, Angle F = 60° (This is correct)

6. **Conclusion:**
- The correct statements based on the congruence of the triangles are:
- DE = 5 cm
- Angle D = 80°
- Angle E = 40°
- Angle F = 60°

### Final Answer:
The correct option that is true based on the congruence of the triangles is that DE = 5 cm, Angle D = 80°, Angle E = 40°, and Angle F = 60°.