Question
△EFG is rotated −90 degrees (clockwise) to create △XYZ . Which of the following statements must be true?(1 point)
Responses which answer is correct and why
EF¯¯¯¯¯¯¯¯≅XZ¯¯¯¯¯¯¯¯
Modifying above upper E upper F with bar congruent to Modifying above upper X upper Z with bar
∠E≅∠X
angle upper E congruent to angle upper X
∠F≅∠Z
angle upper F congruent to angle upper Z
EG¯¯¯¯¯¯¯¯≅XY¯¯¯¯¯¯¯¯
Responses which answer is correct and why
EF¯¯¯¯¯¯¯¯≅XZ¯¯¯¯¯¯¯¯
Modifying above upper E upper F with bar congruent to Modifying above upper X upper Z with bar
∠E≅∠X
angle upper E congruent to angle upper X
∠F≅∠Z
angle upper F congruent to angle upper Z
EG¯¯¯¯¯¯¯¯≅XY¯¯¯¯¯¯¯¯
Answers
GPT-4o mini
When triangle \( \triangle EFG \) is rotated \( -90^\circ \) (clockwise) to create triangle \( \triangle XYZ \), we can analyze each statement in terms of the relationships between corresponding sides and angles after the rotation.
1. **\( \overline{EF} \cong \overline{XZ} \)**: This statement is **not necessarily true** after a \( -90^\circ \) rotation. Triangle \( XYZ \) is created from triangle \( EFG \) by rotation, so the corresponding sides will be equal, but \( EF \) will not align with \( XZ \) after this rotation.
2. **\( \angle E \cong \angle X \)**: This statement is **true**. When triangle \( EFG \) is rotated \( -90^\circ \) to triangle \( XYZ \), the angles maintain their measures and therefore, corresponding angles remain congruent.
3. **\( \angle F \cong \angle Z \)**: This statement is **true** as well. Similar to the reasoning above for angles, the angle \( F \) after rotation will correspond to angle \( Z \), hence they are congruent.
4. **\( \overline{EG} \cong \overline{XY} \)**: This statement is also **true**. The sides remain congruent even after the triangle has been rotated. Thus, \( EG \) will correspond to \( XY \).
Based on the properties of rotation:
- **True Statements:**
- \( \angle E \cong \angle X \)
- \( \angle F \cong \angle Z \)
- \( \overline{EG} \cong \overline{XY} \)
The most definitive statement that "must be true" is that corresponding angles remain congruent after rotation:
- **\( \angle E \cong \angle X \)**
- **\( \angle F \cong \angle Z \)**
Thus, the best answer to choose would be \( \angle E \cong \angle X \).
1. **\( \overline{EF} \cong \overline{XZ} \)**: This statement is **not necessarily true** after a \( -90^\circ \) rotation. Triangle \( XYZ \) is created from triangle \( EFG \) by rotation, so the corresponding sides will be equal, but \( EF \) will not align with \( XZ \) after this rotation.
2. **\( \angle E \cong \angle X \)**: This statement is **true**. When triangle \( EFG \) is rotated \( -90^\circ \) to triangle \( XYZ \), the angles maintain their measures and therefore, corresponding angles remain congruent.
3. **\( \angle F \cong \angle Z \)**: This statement is **true** as well. Similar to the reasoning above for angles, the angle \( F \) after rotation will correspond to angle \( Z \), hence they are congruent.
4. **\( \overline{EG} \cong \overline{XY} \)**: This statement is also **true**. The sides remain congruent even after the triangle has been rotated. Thus, \( EG \) will correspond to \( XY \).
Based on the properties of rotation:
- **True Statements:**
- \( \angle E \cong \angle X \)
- \( \angle F \cong \angle Z \)
- \( \overline{EG} \cong \overline{XY} \)
The most definitive statement that "must be true" is that corresponding angles remain congruent after rotation:
- **\( \angle E \cong \angle X \)**
- **\( \angle F \cong \angle Z \)**
Thus, the best answer to choose would be \( \angle E \cong \angle X \).