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The problem asks why angles \( \angle ABC \) and \( \angle ADC \) in quadrilateral \( BADC \) are congruent. It mentions that \( AB = AD \), \( BC = DC \), and that line \( AC \) is a line of symmetry.

### Analysis:
- Since \( AB = AD \) and \( BC = DC \), quadrilateral \( BADC \) is symmetric along line \( AC \). 
- A line of symmetry implies that corresponding parts across the line are congruent.
- \( \angle ABC \) and \( \angle ADC \) are on either side of the line of symmetry, so they are mirror images of each other. 

### Answer:
The correct statement that explains why \( \angle ABC \) and \( \angle ADC \) are congruent is:  
**"The angles are reflections of each other."**

Would you like more details on how lines of symmetry work in geometric shapes? Here are some follow-up questions to deepen your understanding:

1. What other properties can be derived when a quadrilateral has a line of symmetry?
2. How can we use symmetry to solve problems involving distances or angles in other shapes?
3. If \( \angle ABC \) and \( \angle ADC \) were not congruent, what geometric properties would change?
4. Can a quadrilateral have more than one line of symmetry? Which types of quadrilaterals?
5. How does the congruence of sides help prove that the angles are reflections?

**Tip**: Symmetry often simplifies geometric problems by reducing the number of unique elements you need to analyze.

In quadrilateral BADC, AB = AD and BC = DC. The line AC is a line of symmetry for this quadrilateral. Which of the following statements best explains why angles ABC and ADC are congruent?

In this geometry problem, we explore why angles ABC and ADC in quadrilateral BADC are congruent, given that the quadrilateral is symmetric along line AC. The concepts of symmetry and congruence are explained in detail, suitable for students in grades 6-8.

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