It is given that ABC ∆DEF. Is it true to say that AB = EF? Justify your 
answer.

No, it is **not necessarily true** to say that \( AB = EF \).

Here’s why:

The statement **"ABC ∆DEF"** typically means that triangles \( \triangle ABC \) and \( \triangle DEF \) are congruent or similar, depending on the notation used. However, without a clear indication of whether the triangles are **congruent** or **similar**, we must consider both cases:

1. **If the triangles are congruent**:
   - Congruent triangles have all corresponding sides and angles equal.
   - In this case, it would be true that \( AB = DE \), \( BC = EF \), and \( CA = FD \).
   - Therefore, if \( \triangle ABC \cong \triangle DEF \), **the sides \( AB \) and \( EF \) are not necessarily equal** because \( AB \) corresponds to \( DE \), not \( EF \).

2. **If the triangles are similar**:
   - Similar triangles have corresponding angles equal, but the corresponding sides are proportional, not necessarily equal.
   - In this case, \( AB \) could be proportional to \( DE \), and \( EF \) could be proportional to another side of \( \triangle ABC \), but again, it is **not necessarily true** that \( AB = EF \).

### Conclusion:
The statement \( AB = EF \) is generally **false**, as \( AB \) corresponds to \( DE \) in both congruent and similar triangles, not to \( EF \).

Would you like more clarification on congruent vs. similar triangles or proportionality? 

Here are five related questions for deeper exploration:
1. How do you determine if two triangles are congruent?
2. What are the criteria for two triangles to be similar?
3. What is the significance of corresponding sides in congruent triangles?
4. How do you find the ratio of corresponding sides in similar triangles?
5. Can two triangles have equal angles but not be congruent?

**Tip**: When working with triangles, always pay attention to the correspondence of sides and angles to avoid mismatches in equalities.

It is given that ABC ∆DEF. Is it true to say that AB = EF? Justify your answer.

Explore the relationship between corresponding sides in congruent and similar triangles through the question: 'Is it true to say that AB = EF?' This problem emphasizes key concepts in congruence and similarity, suitable for students in Grades 8-10.

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