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

Question

Responses

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

∠E≅∠X
angle upper E congruent to angle upper X

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

EF¯¯¯¯¯¯¯¯≅XZ¯¯¯¯¯¯¯¯

Answer 1

To analyze the transformation of triangle \( \triangle EFG \) when it is rotated \( -90^\circ \) (clockwise) to become triangle \( \triangle XYZ \), we need to understand the relationships between the sides and angles of the two triangles after the transformation.

1. EG ≅ XY: This statement is not necessarily true. In a rotation, the length of corresponding segments remains equal, so while segment \( EG \) might correspond to segment \( XY \), it’s necessary to check the correspondence after considering the points' new locations upon rotation.

2. ∠E ≅ ∠X: This statement is not true. The angle at point E in triangle EFG does not correspond to the angle at point X in triangle XYZ after a \( -90^\circ \) rotation.

3. ∠F ≅ ∠Z: This statement is true. Under a \( -90^\circ \) clockwise rotation, the angle at point F will correspond to the angle at point Z since the original triangle's angles remain congruent under rotation.

4. EF ≅ XZ: This statement is not necessarily true. While the lengths of corresponding sides remain the same, EF corresponds to a different segment (XZ) in the rotated triangle, so it must be confirmed based on specific points' locations, though generally it’s true after correct rotation.

From the choices, the only statement that must be true regarding the relationship between the angles in triangles \( \triangle EFG \) and \( \triangle XYZ \) after the \( -90^\circ \) rotation is:

∠F ≅ ∠Z.