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△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 choose only one answer solve it and tell me if it is the right one or not

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¯¯¯¯¯¯¯¯

1 answer

To determine which statement must be true when triangle \( \triangle EFG \) is rotated \( -90 \) degrees (clockwise) to create triangle \( \triangle XYZ \), we need to understand the properties of rotation in geometry.

When a figure is rotated:

  1. The lengths of the sides remain the same.
  2. The angles remain the same.
  3. The orientation of the triangle changes.

Now let's evaluate each of the statements one by one to see which one must be true:

  1. \( EF \cong XZ \): This statement cannot be guaranteed true because the segment \( EF \) does not correspond to segment \( XZ \) in the notation of rotation. In a \( -90^\circ \) rotation, point \( E \) would correspond to point \( Y \), \( F \) would correspond to point \( Z \), and \( G \) would correspond to point \( X \).

  2. \( \angle E \cong \angle X \): In a \( -90^\circ \) rotation, the angles are preserved. However, the angle \( E \) corresponds to angle \( Y \) after rotation, not angle \( X \). Therefore, this statement is also not true.

  3. \( \angle F \cong \angle Z \): As determined previously, angle \( F \) corresponds to angle \( Z \). Since rotations preserve angle measures, this statement is true.

  4. \( EG \cong XY \): Similar to the reasoning for \( EF \) and \( XZ \), \( EG \) does not correspond to \( XY \) after the rotation, so this statement cannot be taken as true.

Conclusion: The correct answer is \( \angle F \cong \angle Z \) because when triangle \( EFG \) is rotated \( -90^\circ \), angle \( F \) directly corresponds to angle \( Z \) after the transformation. Thus, this statement must be true.