Quadrilateral *ABCD* is reflected across the *x*-axis. Quadrilateral *HGFE* is the image of the reflection.

Which angles must be congruent?

A.

∠D≅∠H∠D≅∠H

B.

∠E≅∠A∠E≅∠A

C.

∠E≅∠B∠E≅∠B

D.

∠F≅∠C∠F≅∠C

When a figure is reflected across the x-axis, each point on the figure moves to a corresponding point directly opposite it on the other side of the axis, preserving distances and angles. Since reflections preserve the shapes and sizes of figures, corresponding angles of the original and the reflected image will be congruent.

Given that quadrilateral ABCD is reflected to form quadrilateral HGFE, the corresponding angles will be congruent based on the order of the vertices:

1. **∠A corresponds to ∠E**
2. **∠B corresponds to ∠F**
3. **∠C corresponds to ∠G**
4. **∠D corresponds to ∠H**

Therefore, the correct matching of congruent angles is:

- **Option D: ∠F ≅ ∠C**

This is because ∠F is the reflection of ∠C across the x-axis, making them congruent.

Would you like a more detailed explanation or have any questions?

### Related Questions:
1. How does reflection affect the orientation of a shape?
2. What are the properties preserved during a reflection?
3. How do you find the coordinates of a reflected point across the x-axis?
4. How does reflecting a shape across the y-axis differ from reflecting across the x-axis?
5. What are other transformations that preserve congruence of angles?

**Tip:** Reflections across an axis always result in a "mirror image," flipping the figure while preserving shape and size.

Quadrilateral ABCD is reflected across the x-axis. Quadrilateral HGFE is the image of the reflection. Which angles must be congruent? A. ∠D ≅ ∠H B. ∠E ≅ ∠A C. ∠E ≅ ∠B D. ∠F ≅ ∠C

Understand which angles are congruent when quadrilateral ABCD is reflected across the x-axis to form quadrilateral HGFE. Learn the concepts of reflections, congruence, and how transformations preserve angles and distances. Suitable for students in Grades 6-8.

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