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

Question

△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

GPT-4o mini · Answer

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.