Asked by hihi
△EFG is rotated −90 degrees (clockwise) to create △XYZ . Which of the following statements must be true?(1 point)
Responses
EF≅XZ
∠E≅∠X
angle upper E congruent to angle upper X
EG≅XY
∠F≅∠Z
Responses
EF≅XZ
∠E≅∠X
angle upper E congruent to angle upper X
EG≅XY
∠F≅∠Z
Answers
Answered by
GPT-4o mini
When triangle \( \triangle EFG \) is rotated \( -90 \) degrees (clockwise) to create triangle \( \triangle XYZ \), the following properties apply:
1. **Congruence of sides**: The sides of the original triangle will be congruent to the sides of the rotated triangle. Therefore, \( EF \) will be congruent to \( XZ \), and \( EG \) will be congruent to \( XY \).
2. **Congruence of angles**: The angles of triangle \( \triangle EFG \) will also be congruent to the angles of triangle \( \triangle XYZ \) after the rotation. Thus, \( \angle E \) will be congruent to \( \angle X \), and \( \angle F \) will be congruent to \( \angle Z \).
Given these properties, the following statements must be true:
- \( EF \cong XZ \)
- \( \angle E \cong \angle X \)
- \( EG \cong XY \)
- \( \angle F \cong \angle Z \)
Since the question asks which statements must be true, all the statements provided in your options must be true based on the properties of congruence and rotation.
1. **Congruence of sides**: The sides of the original triangle will be congruent to the sides of the rotated triangle. Therefore, \( EF \) will be congruent to \( XZ \), and \( EG \) will be congruent to \( XY \).
2. **Congruence of angles**: The angles of triangle \( \triangle EFG \) will also be congruent to the angles of triangle \( \triangle XYZ \) after the rotation. Thus, \( \angle E \) will be congruent to \( \angle X \), and \( \angle F \) will be congruent to \( \angle Z \).
Given these properties, the following statements must be true:
- \( EF \cong XZ \)
- \( \angle E \cong \angle X \)
- \( EG \cong XY \)
- \( \angle F \cong \angle Z \)
Since the question asks which statements must be true, all the statements provided in your options must be true based on the properties of congruence and rotation.