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The problem asks for a true statement given that \(\triangle EHG \cong \triangle KFC\). Since the triangles are congruent, corresponding sides and angles must be congruent.

Let’s break it down:

1. **Corresponding angles**:  
   From \(\triangle EHG \cong \triangle KFC\), we know the following:
   - \(\angle E \cong \angle K\)
   - \(\angle H \cong \angle F\)
   - \(\angle G \cong \angle C\)

2. **Corresponding sides**:
   - \(EH \cong KF\)
   - \(HG \cong FC\)
   - \(EG \cong KC\)

Now, looking at the answer choices:
- **Option 1: \( HG \cong KF \)**  
  This is incorrect because \(HG\) corresponds to \(FC\), not \(KF\).
  
- **Option 2: \( EG \cong KC \)**  
  This is correct since \(EG\) corresponds to \(KC\).

- **Option 3: \( \angle E \cong \angle C \)**  
  This is incorrect because \(\angle E\) corresponds to \(\angle K\), not \(\angle C\).

- **Option 4: \( EH \cong KC \)**  
  This is incorrect because \(EH\) corresponds to \(KF\), not \(KC\).

Thus, the correct answer is **Option 2: \( EG \cong KC \)**.

Would you like further details or have any other questions?

Here are some related questions:
1. What is the definition of congruent triangles?
2. How do you identify corresponding sides in congruent triangles?
3. Can two triangles be congruent without having all their sides equal?
4. How does the angle-side relationship work in congruent triangles?
5. What are other ways to prove that two triangles are congruent?

**Tip:** Always ensure that corresponding parts (angles and sides) of congruent triangles are correctly identified when analyzing geometric problems.

If \(\triangle EHG \cong \triangle KFC\), which of the following is a true statement?
- HG ≅ KF
- EG ≅ KC
- ∠E ≅ ∠C
- EH ≅ KC

Learn how to identify the true corresponding sides and angles in congruent triangles with this problem involving \(\triangle EHG \cong \triangle KFC\). This solution explains the key concepts of congruent triangles and corresponding parts. Suitable for students in Grades 8-10.

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