In `DeltaABC `and `DeltaDEF`, if `/_A = 50^@,/_B = 70^@, /_C = 60^@, /_D = 60^@, /_E = 70^@ and /_F = 50^@`, then

Options

A. `DeltaABC ~ DeltaFED`
B. `DeltaABC ~ DeltaDFE`
C. `DeltaABC ~ DeltaEDF`
D. `DeltaABC ~ DeltaDEF `

Answer

To solve the problem, we need to analyze the angles of the two triangles, ΔABC and ΔDEF, and determine if they are similar based on their angle measures.

### Step-by-Step Solution:

1. **Identify the Angles of Triangle ABC:**
- Angle A = 50°
- Angle B = 70°
- Angle C = 60°

2. **Identify the Angles of Triangle DEF:**
- Angle D = 60°
- Angle E = 70°
- Angle F = 50°

3. **List the Angles in Order:**
- For triangle ABC: A = 50°, B = 70°, C = 60°
- For triangle DEF: D = 60°, E = 70°, F = 50°

4. **Check for Angle Correspondence:**
- Compare the angles:
- A (50°) corresponds to F (50°)
- B (70°) corresponds to E (70°)
- C (60°) corresponds to D (60°)

5. **Determine Similarity:**
- Since the angles of triangle ABC correspond to the angles of triangle DEF, we can conclude that:
- ΔABC ∼ ΔDEF (Triangle ABC is similar to Triangle DEF).

### Conclusion:
The two triangles are similar because their corresponding angles are equal.

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