In `Delta ABC `and `DeltaDEF, AB = DE and BC = EF`. Then one can infer that
`Delta ABC = Delta DEF`, when

Options

A. `/_BAC = /_EDF `
B. `/_ACB = /_EDF `
C. `/_ACB = /_DFE `
D. `/_ABC = /_DEF `

Answer

To determine when triangles ABC and DEF are congruent given that AB = DE and BC = EF, we can follow these steps:

### Step-by-Step Solution:

1. **Identify Given Information**:
We know that:
- AB = DE (one pair of corresponding sides)
- BC = EF (another pair of corresponding sides)

2. **Understand Triangle Congruence**:
For two triangles to be congruent, they must satisfy certain conditions. One of the common conditions is the Side-Angle-Side (SAS) congruence criterion.

3. **Apply the SAS Congruence Criterion**:
According to the SAS criterion, if two sides of one triangle are equal to two sides of another triangle, and the angle included between those sides is equal, then the two triangles are congruent.

4. **Determine the Required Angle**:
In our case, we need to ensure that the angle between the sides AB and BC in triangle ABC is equal to the angle between the sides DE and EF in triangle DEF.
- Specifically, we need to show that angle ABC = angle DEF.

5. **Conclusion**:
Therefore, triangle ABC is congruent to triangle DEF if:
- AB = DE
- BC = EF
- Angle ABC = Angle DEF

### Final Answer:
Triangle ABC is congruent to triangle DEF when angle ABC = angle DEF.

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