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The image shows a triangle \( \triangle ABC \), where \( \angle A \cong \angle C \). The problem asks which of the following conclusions is true given this information.

### Options:
1. \( AC \cong BC \)
2. \( AB \cong BC \)
3. \( \angle C \cong \angle B \)
4. \( \angle A \cong \angle B \)

### Solution:
If \( \angle A \cong \angle C \), the triangle \( \triangle ABC \) is isosceles with the base \( AB \). In an isosceles triangle, the two angles opposite the equal sides are congruent. Therefore, sides \( AB \) and \( BC \) must be congruent because these sides are opposite the congruent angles \( \angle A \) and \( \angle C \).

Thus, the correct conclusion is:
- \( AB \cong BC \) (Option 2).

Would you like further details or explanations on this? 

Here are 5 related questions to explore:
1. How do you identify congruent triangles?
2. What is the relationship between angles and sides in isosceles triangles?
3. How can you prove triangles are congruent using angle-side relationships?
4. How does the Isosceles Triangle Theorem help in solving such problems?
5. What are other common properties of isosceles triangles?

**Tip:** In an isosceles triangle, the two angles opposite the equal sides are always congruent, and this can often help in solving triangle problems.

If ∠A ≅ ∠C, then which of the following conclusions is true?

Analyze triangle ABC where ∠A ≅ ∠C. Using the Isosceles Triangle Theorem, determine which side or angle relationships are true. This geometry problem focuses on triangle congruence and is ideal for students in Grades 8-10.

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