Question

△EFG is rotated −90 degrees (clockwise) to create △XYZ . Which of the following statements must be true?(1 point)%0D%0AResponses%0D%0A%0D%0AEG¯¯¯¯¯¯¯¯≅XY¯¯¯¯¯¯¯¯%0D%0AModifying above upper E upper G with bar congruent to Modifying above upper X upper Y with bar%0D%0A%0D%0A∠E≅∠X %0D%0Aangle upper E congruent to angle upper X%0D%0A%0D%0AEF¯¯¯¯¯¯¯¯≅XZ¯¯¯¯¯¯¯¯%0D%0AModifying above upper E upper F with bar congruent to Modifying above upper X upper Z with bar%0D%0A%0D%0A∠F≅∠Z

Answer 1

When a triangle is rotated, the corresponding sides and angles retain their relationships. In the case of triangle \( \triangle EFG \) being rotated \(-90\) degrees (clockwise) to create triangle \( \triangle XYZ \), the following statements must be true:

1. \( \overline{EG} \cong \overline{XY} \): This statement is true because the side \( \overline{EG} \) corresponds to side \( \overline{XY} \) after the rotation.

2. \( \angle E \cong \angle X \): This statement is true, as the angle \( \angle E \) corresponds to angle \( \angle X \) after rotation.

3. \( \overline{EF} \cong \overline{XZ} \): This statement is also true because the segment \( \overline{EF} \) corresponds to segment \( \overline{XZ} \) after the rotation.

4. \( \angle F \cong \angle Z \): This statement must also be true since angle \( \angle F \) corresponds to angle \( \angle Z \).

In summary, all the statements about the congruences of sides and corresponding angles in the rotated triangles are true:

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

Therefore, any of these statements can be selected since they all hold true under the rotation.

Answer 2

which one is the answer?

Answer 3

To determine which specific statement must be true after the rotation of triangle \( \triangle EFG \) to triangle \( \triangle XYZ \), we can evaluate the statements one by one:

1. \( \overline{EG} \cong \overline{XY} \): This statement is true.

2. \( \angle E \cong \angle X \): This statement is true.

3. \( \overline{EF} \cong \overline{XZ} \): This statement is true.

4. \( \angle F \cong \angle Z \): This statement is true.

However, only one option can be provided in response as the answer. If you are looking for one answer, you can choose any of the statements listed above, but typically the first mentioned is selected.

Therefore, the answer you might want to present is:

\( \overline{EG} \cong \overline{XY} \) (first statement).

This is based on the correspondence established during the rotation.