Question
△EFG
is rotated −90
degrees (clockwise) to create △XYZ
. Which of the following statements must be true?(1 point)
Responses
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
angle upper F congruent to angle upper Z
∠E≅∠X
is rotated −90
degrees (clockwise) to create △XYZ
. Which of the following statements must be true?(1 point)
Responses
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
angle upper F congruent to angle upper Z
∠E≅∠X
Answers
GPT-4o mini
When triangle \( \triangle EFG \) is rotated \(-90\) degrees (clockwise) to create triangle \( \triangle XYZ \), we can determine the relationships between corresponding sides and angles.
1. **Rotating \(-90\) degrees clockwise:**
- The point \(E\) moves to point \(Y\).
- The point \(F\) moves to point \(Z\).
- The point \(G\) moves to point \(X\).
2. **Corresponding Sides:**
- The side \(EG\) corresponds to side \(XY\).
- The side \(EF\) corresponds to side \(XZ\).
- The side \(FG\) corresponds to side \(YZ\).
3. **Corresponding Angles:**
- Angle \(F\) corresponds to angle \(Z\).
- Angle \(E\) corresponds to angle \(Y\).
- Angle \(G\) corresponds to angle \(X\).
Based on this information, the following statements must be true:
- **\(EG \cong XY\)**: Since side \(EG\) corresponds to side \(XY\), they are congruent.
- **\(EF \cong XZ\)**: Since side \(EF\) corresponds to side \(XZ\), they are also congruent.
- **\(\angle F \cong \angle Z\)**: Since angle \(F\) corresponds to angle \(Z\), they are congruent.
- **\(\angle E \cong \angle Y\)**: Since angle \(E\) corresponds to angle \(Y\), they are congruent.
In conclusion, all statements provided correspond to the necessary congruences resulting from the rotation. Therefore, the statements that must be true are:
- **\(EG \cong XY\)**
- **\(EF \cong XZ\)**
- **\(\angle F \cong \angle Z\)**
- **\(\angle E \cong \angle X\)**
However, you should choose any correct statement based on the options provided, such as \(\angle F \cong \angle Z\) and others mentioned above.
1. **Rotating \(-90\) degrees clockwise:**
- The point \(E\) moves to point \(Y\).
- The point \(F\) moves to point \(Z\).
- The point \(G\) moves to point \(X\).
2. **Corresponding Sides:**
- The side \(EG\) corresponds to side \(XY\).
- The side \(EF\) corresponds to side \(XZ\).
- The side \(FG\) corresponds to side \(YZ\).
3. **Corresponding Angles:**
- Angle \(F\) corresponds to angle \(Z\).
- Angle \(E\) corresponds to angle \(Y\).
- Angle \(G\) corresponds to angle \(X\).
Based on this information, the following statements must be true:
- **\(EG \cong XY\)**: Since side \(EG\) corresponds to side \(XY\), they are congruent.
- **\(EF \cong XZ\)**: Since side \(EF\) corresponds to side \(XZ\), they are also congruent.
- **\(\angle F \cong \angle Z\)**: Since angle \(F\) corresponds to angle \(Z\), they are congruent.
- **\(\angle E \cong \angle Y\)**: Since angle \(E\) corresponds to angle \(Y\), they are congruent.
In conclusion, all statements provided correspond to the necessary congruences resulting from the rotation. Therefore, the statements that must be true are:
- **\(EG \cong XY\)**
- **\(EF \cong XZ\)**
- **\(\angle F \cong \angle Z\)**
- **\(\angle E \cong \angle X\)**
However, you should choose any correct statement based on the options provided, such as \(\angle F \cong \angle Z\) and others mentioned above.