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

Question

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

EF¯¯¯¯¯¯¯¯≅XZ¯¯¯¯¯¯¯¯
Modifying above upper E upper F with bar congruent to Modifying above upper X upper Z with bar

∠F≅∠Z

Answer 1

When triangle \( \triangle EFG \) is rotated \(-90\) degrees (clockwise) to create triangle \( \triangle XYZ \), the properties of rotation in geometry can be analyzed to determine which statements must be true.

1. \( \angle E \cong \angle X \): This statement must be true. Under a rotation, angles are preserved, meaning that corresponding angles in the new triangle will be congruent to those in the original triangle.

2. \( \overline{EG} \cong \overline{XY} \): This statement must also be true. The lengths of the sides are preserved under rotation, so corresponding sides will be congruent.

3. \( \overline{EF} \cong \overline{XZ} \): This statement must be true as well for the same reason as above—side lengths are preserved under rotation.

4. \( \angle F \cong \angle Z \): This statement must be true. Similar to the measurement of angles, the rotation does not change their measures, and consequently angles that correspond will remain congruent.

Thus, all of the options are true:

• \( \angle E \cong \angle X \)
• \( \overline{EG} \cong \overline{XY} \)
• \( \overline{EF} \cong \overline{XZ} \)
• \( \angle F \cong \angle Z \)

Therefore, the conclusion is that all statements must be true. However, since the question seems to ask which statements must necessarily be true with regard to the rotation's effect, you can choose any of the statements listed above as true.