Question

△EFG is rotated −90 degrees (clockwise) to create △XYZ . Which of the following statements must be true?(1 point)
Responses

EF¯¯¯¯¯¯¯¯≅XZ¯¯¯¯¯¯¯¯
Modifying above upper E upper F with bar congruent to Modifying above upper X upper Z with bar

∠F≅∠Z
angle upper F congruent to angle upper Z

EG¯¯¯¯¯¯¯¯≅XY¯¯¯¯¯¯¯¯
Modifying above upper E upper G with bar congruent to Modifying above upper X upper Y with bar

∠E≅∠X

Answer 1

When a triangle \( \triangle EFG \) is rotated \(-90\) degrees (clockwise) to form triangle \( \triangle XYZ \), we can analyze the relationship between the corresponding sides and angles of the two triangles.

1. **Sides**: Under a rotation, corresponding sides of triangles remain congruent. Therefore:
- \( \overline{EF} \cong \overline{XZ} \)
- \( \overline{EG} \cong \overline{XY} \)
- \( \overline{FG} \cong \overline{YZ} \)

2. **Angles**: Similarly, corresponding angles remain congruent after rotation:
- \( \angle E \cong \angle X \)
- \( \angle F \cong \angle Z \)
- \( \angle G \cong \angle Y \)

Now, considering the specific statements given:

1. **\( \overline{EF} \cong \overline{XZ} \)** - This statement **is true**.
2. **\( \angle F \cong \angle Z \)** - This statement **is true**.
3. **\( \overline{EG} \cong \overline{XY} \)** - This statement **is true**.
4. **\( \angle E \cong \angle X \)** - This statement **is also true**.

All these options convey properties that are preserved during the rotation of the triangles.

Overall, all four statements must be true based on the properties of rotation in geometry. However, if you have to select the must-be-true statement from your options, any of the first three regarding sides or angles would be acceptable.

In conclusion, here are the answers that must be true:
- \( \overline{EF} \cong \overline{XZ} \)
- \( \angle F \cong \angle Z \)
- \( \overline{EG} \cong \overline{XY} \)
- \( \angle E \cong \angle X \)

Any of the first three statements regarding congruence of sides or angles after the rotation hold true.