Question
△EFG is rotated −90 degrees (clockwise) to create △XYZ . Which of the following statements must be true?(1 point)
Responses a b c or d which one is it
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
angle upper E congruent to angle upper X
Responses a b c or d which one is it
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
angle upper E congruent to angle upper X
Answers
Answered by
GPT-4o mini
When triangle \( \triangle EFG \) is rotated \( -90 \) degrees clockwise to create triangle \( \triangle XYZ \), we can analyze how the vertices and sides correspond to each other after the rotation.
1. **Vertex Correspondence**:
- After a \( -90 \) degree clockwise rotation:
- Point \( E \) moves to point \( X \).
- Point \( F \) moves to point \( Y \).
- Point \( G \) moves to point \( Z \).
2. **Side Correspondence**:
- The side \( \overline{EG} \) corresponds to the side \( \overline{XY} \).
- The side \( \overline{EF} \) corresponds to the side \( \overline{XZ} \).
- The side \( \overline{FG} \) corresponds to the side \( \overline{YZ} \).
3. **Angle Correspondence**:
- Angle \( \angle E \) corresponds to angle \( \angle X \).
- Angle \( \angle F \) corresponds to angle \( \angle Y \).
- Angle \( \angle G \) corresponds to angle \( \angle Z \).
Based on the above analysis, we can evaluate the given statements:
- **A.** \( \overline{EG} \cong \overline{XY} \) - This statement is **not true**. The correct correspondence is \( \overline{EG} \cong \overline{XZ} \).
- **B.** \( \overline{EF} \cong \overline{XZ} \) - This is **true** as \( \overline{EF} \) and \( \overline{XZ} \) correspond after the rotation.
- **C.** \( \angle F \cong \angle Z \) - This is **true** since angle \( F \) corresponds to \( Y \), and not \( Z \). Thus, this statement is **not true**.
- **D.** \( \angle E \cong \angle X \) - This is **true** as angle \( E \) corresponds directly to angle \( X \).
Thus, the statements that must be true after the rotation are:
- **B** (correct side congruence, \( \overline{EF} \cong \overline{XZ} \)),
- **D** (angle congruence, \( \angle E \cong \angle X \)).
For the purpose of your question, if you are looking for one specific choice, **B** is the most relevant one asserting a congruence among sides.
1. **Vertex Correspondence**:
- After a \( -90 \) degree clockwise rotation:
- Point \( E \) moves to point \( X \).
- Point \( F \) moves to point \( Y \).
- Point \( G \) moves to point \( Z \).
2. **Side Correspondence**:
- The side \( \overline{EG} \) corresponds to the side \( \overline{XY} \).
- The side \( \overline{EF} \) corresponds to the side \( \overline{XZ} \).
- The side \( \overline{FG} \) corresponds to the side \( \overline{YZ} \).
3. **Angle Correspondence**:
- Angle \( \angle E \) corresponds to angle \( \angle X \).
- Angle \( \angle F \) corresponds to angle \( \angle Y \).
- Angle \( \angle G \) corresponds to angle \( \angle Z \).
Based on the above analysis, we can evaluate the given statements:
- **A.** \( \overline{EG} \cong \overline{XY} \) - This statement is **not true**. The correct correspondence is \( \overline{EG} \cong \overline{XZ} \).
- **B.** \( \overline{EF} \cong \overline{XZ} \) - This is **true** as \( \overline{EF} \) and \( \overline{XZ} \) correspond after the rotation.
- **C.** \( \angle F \cong \angle Z \) - This is **true** since angle \( F \) corresponds to \( Y \), and not \( Z \). Thus, this statement is **not true**.
- **D.** \( \angle E \cong \angle X \) - This is **true** as angle \( E \) corresponds directly to angle \( X \).
Thus, the statements that must be true after the rotation are:
- **B** (correct side congruence, \( \overline{EF} \cong \overline{XZ} \)),
- **D** (angle congruence, \( \angle E \cong \angle X \)).
For the purpose of your question, if you are looking for one specific choice, **B** is the most relevant one asserting a congruence among sides.