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,angel D = 60^(@)`

Explanation

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

### 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 given are:
- AB = 5 cm
- ∠B = 40°
- ∠A = 80°

2. **Determine the Third Angle of Triangle ABC**:
- We can find the third angle, ∠C, using the angle sum property of triangles, which states that the sum of the angles in a triangle is 180°.
- Therefore, we calculate:
\[ \angle C = 180° - \angle A - \angle B \]
\[ \angle C = 180° - 80° - 40° = 60° \]

3. **Use the Properties of Congruent Triangles**:
- Since ΔABC ≅ ΔFDE, the corresponding angles and sides of the triangles are equal.
- This means:
- ∠E = ∠C = 60°
- ∠F = ∠A = 80°
- AB = FD (corresponding sides) = 5 cm

4. **Conclusion about the Sides and Angles**:
- From the above, we can conclude:
- FD = 5 cm (since AB = 5 cm)
- ∠E = 60°
- ∠F = 80°

5. **Identify the Correct Option**:
- We need to determine which of the given options is true based on the calculated values.
- Since we have established that:
- FD = 5 cm
- ∠E = 60°
- ∠F = 80°
- The correct option must reflect that FD = 5 cm and ∠E = 60°.

### Final Answer:
The correct option is that FD = 5 cm and ∠E = 60°.