Question
△EFG is rotated −90 degrees (clockwise) to create △XYZ . Which of the following statements must be true?(1 point)
Responses which one is answer is correct and why
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¯¯¯¯¯¯¯¯
Responses which one is answer is correct and why
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¯¯¯¯¯¯¯¯
Answers
Answered by
GPT-4o mini
When a triangle is rotated, the following properties hold true:
1. **Corresponding sides of the triangles after rotation are congruent**.
2. **Corresponding angles of the triangles after rotation are congruent**.
Given that △EFG is rotated −90 degrees (clockwise) to create △XYZ, let's analyze the statements:
1. **\( \overline{EF} \cong \overline{XZ} \)**: This statement is **not necessarily true** because after a clockwise rotation, the sides might not correspond in this way.
2. **\( \angle E \cong \angle X \)**: This statement is **not true** because when triangle EFG is rotated -90 degrees, angle E will correspond to angle Z, not X.
3. **\( \angle F \cong \angle Z \)**: This statement is **true**. During a -90-degree rotation, angle F moves to the position of angle Z, thus they are congruent.
4. **\( \overline{EG} \cong \overline{XY} \)**: This statement is also **not necessarily true** for the same reason as the first point; EG does not correspond with XY after the rotation.
Among the given options, the correct statement is:
**∠F ≅ ∠Z**
This statement must be true after a -90 degree clockwise rotation.
1. **Corresponding sides of the triangles after rotation are congruent**.
2. **Corresponding angles of the triangles after rotation are congruent**.
Given that △EFG is rotated −90 degrees (clockwise) to create △XYZ, let's analyze the statements:
1. **\( \overline{EF} \cong \overline{XZ} \)**: This statement is **not necessarily true** because after a clockwise rotation, the sides might not correspond in this way.
2. **\( \angle E \cong \angle X \)**: This statement is **not true** because when triangle EFG is rotated -90 degrees, angle E will correspond to angle Z, not X.
3. **\( \angle F \cong \angle Z \)**: This statement is **true**. During a -90-degree rotation, angle F moves to the position of angle Z, thus they are congruent.
4. **\( \overline{EG} \cong \overline{XY} \)**: This statement is also **not necessarily true** for the same reason as the first point; EG does not correspond with XY after the rotation.
Among the given options, the correct statement is:
**∠F ≅ ∠Z**
This statement must be true after a -90 degree clockwise rotation.