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Question △EFG is rotated −90 degrees (clockwise) to create △XYZ . Which of the following statements must be true?(1 point) Responses ∠E≅∠X angle upper E congruent to angle upper X EG¯¯¯¯¯¯¯¯≅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 EF¯¯¯¯¯¯¯¯≅XZ¯¯¯¯¯¯¯¯ Modifying above upper E upper F with bar congruent to Modifying above upper X upper Z with bar Skip to navigation

1 answer

When triangle \( △EFG \) is rotated \(-90\) degrees (clockwise) to create triangle \( △XYZ \), several properties are preserved due to the nature of rotation, which is a rigid transformation. This means that lengths and angles remain congruent.

Given this information, let's analyze the statements:

  1. \( \angle E \cong \angle X \): This statement must be true. When triangle \( EF \) is rotated \(-90\) degrees to form triangle \( XYZ \), the angles remain congruent.

  2. \( \overline{EG} \cong \overline{XY} \): This statement must also be true. The sides will remain congruent under rotation.

  3. \( \angle F \cong \angle Z \): This statement must be true as well, for the same reason as angle E and angle X.

  4. \( \overline{EF} \cong \overline{XZ} \): This statement must likewise be true, as the lengths of the sides will remain invariant under rotation.

Thus, all statements provided (1 through 4) must be true due to the properties of geometric rotations.