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

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¯¯¯¯¯¯¯¯
Modifying above upper E upper G with bar congruent to Modifying above upper X upper Y with bar
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1 answer

When triangle \( \triangle EFG \) is rotated \(-90\) degrees clockwise to create triangle \( \triangle XYZ \), we can analyze the congruences of the sides and angles based on the properties of rotation.

  1. Side congruences: Rotation preserves distances, meaning that the length of segments is unchanged. Therefore:

    • \( \overline{EF} \) will be congruent to \( \overline{XZ} \) after the rotation.
    • \( \overline{EG} \) will be congruent to \( \overline{XY} \) after the rotation.
    • \( \overline{FG} \) will be congruent to \( \overline{YZ} \).

  2. Angle congruences: Rotation also preserves the measures of angles. After a rotation of \(-90\) degrees:

    • The angle at point \( E \) will correspond to the angle at point \( X \).
    • The angle at point \( F \) will correspond to the angle at point \( Z \).
    • The angle at point \( G \) will correspond to the angle at point \( Y \).

From the statements given:

  • Statement 1: \( \overline{EF} \cong \overline{XZ} \) - True, based on the properties of rotation.
  • Statement 2: \( \angle E \cong \angle X \) - True, since \( \angle E \) corresponds to \( \angle X \) after the rotation.
  • Statement 3: \( \angle F \cong \angle Z \) - True, as \( \angle F \) corresponds to \( \angle Z \) after the rotation.
  • Statement 4: \( \overline{EG} \cong \overline{XY} \) - True, based on the properties of rotation.

Since all these statements are based on the congruence that holds after rotation, any of these statements could be considered true. However, what is critical is how you interpret the question asking for "which of the following statements must be true.” All statements listed can stand true due to rotational congruences.

In conclusion, all the given statements must be true given the conditions of the problem, but particularly the first angle congruences and side lengths must always correspond to their rotated counterparts.