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△EFG is rotated −90 degrees (clockwise) to create △XYZ . Which of the following statements must be true?(1 point)ResponsesEF¯¯¯¯¯¯¯¯≅XZ¯¯¯¯¯¯¯¯Modifying above upper E upper F with bar congruent to Modifying above upper X upper Z with barEG¯¯¯¯¯¯¯¯≅XY¯¯¯¯¯¯¯¯Modifying above upper E upper G with bar congruent to Modifying above upper X upper Y with bar∠F≅∠Z angle upper F congruent to angle upper Z∠E≅∠X angle upper E congruent to angle upper X

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When triangle \( \triangle EFG \) is rotated -90 degrees (clockwise), the corresponding points in triangle \( \triangle XYZ \) will be transformed as follows:

  • Point \( E \) maps to point \( X \)
  • Point \( F \) maps to point \( Z \)
  • Point \( G \) maps to point \( Y \)

Considering this transformation, we can determine the following statements:

  1. \( \overline{EF} \cong \overline{XZ} \): This statement is not necessarily true. The segments may or may not be congruent depending on the properties of the original triangle and its orientation.

  2. \( \overline{EG} \cong \overline{XY} \): This statement is also not necessarily true for the same reasons as above.

  3. \( \angle F \cong \angle Z \): This statement is true. Rotation preserves the angles of the triangle, so corresponding angles will remain congruent.

  4. \( \angle E \cong \angle X \): This statement is also true for the same reason; the angles remain congruent under rotation.

Thus, the statements that must be true after the rotation are:

  • \( \angle F \cong \angle Z \)
  • \( \angle E \cong \angle X \)

So, the correct true statements are:

  • \( \angle F \cong \angle Z \)
  • \( \angle E \cong \angle X \)