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The question in the image asks why segments \( AD \) and \( AC \) are congruent after triangle \( ABC \) is reflected across line \( AB \), resulting in triangle \( ABD \).

### Explanation:
When a figure is reflected across a line, the reflected image will have congruent corresponding parts to the original figure. In this case, triangle \( ABC \) is reflected across line \( AB \) to form triangle \( ABD \). Since \( AC \) corresponds to \( AD \) in this reflection, these segments are congruent by definition.

### Answer:
The correct choice is **A**: *Congruent parts of congruent figures are corresponding.*

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Do you need further details or have any questions? Here are 5 related questions you might find helpful:

1. What is a reflection in geometry, and how does it affect corresponding points?
2. How do you determine corresponding parts of two triangles?
3. What other properties are preserved under a reflection?
4. Can two triangles have congruent sides but not be congruent? Why or why not?
5. How do you find the perpendicular bisector of a segment?

**Tip:** In geometry, congruent parts of figures are always corresponding parts when a transformation such as reflection, rotation, or translation is applied.

When triangle ABC is reflected across line AB, the image is triangle ABD. Why are segment AD and segment AC congruent?

Learn why segment AD is congruent to segment AC after triangle ABC is reflected across line AB. This geometry problem explains congruence of corresponding parts and the properties of reflections. Suitable for Grades 9-10.

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