Question
there is only one correct answer and eliminate the rest that are false
△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
angle upper E congruent to angle upper X
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△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
angle upper E congruent to angle upper X
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Answers
GPT-4o mini
When triangle \( \triangle EFG \) is rotated \( -90 \) degrees (clockwise) to form \( \triangle XYZ \), the corresponding segments and angles will transform according to the rotation.
1. **Understanding the rotation:**
- A \( -90 \) degree clockwise rotation can be interpreted through the following point transformation:
- \( (x, y) \) becomes \( (y, -x) \).
- Therefore, the vertex relationships change as follows:
- Point \( E \) rotates to point \( Y \).
- Point \( F \) rotates to point \( Z \).
- Point \( G \) rotates to point \( X \).
2. **Analyzing the statements:**
- **Statement 1: \( \overline{EG} \cong \overline{XY} \)**
- **False.** Since \( G \) rotates to \( X \), this segment does not represent congruence.
- **Statement 2: \( \overline{EF} \cong \overline{XZ} \)**
- **False.** \( F \) goes to \( Z \) and does not support this congruence.
- **Statement 3: \( \angle F \cong \angle Z \)**
- **True.** Angles corresponding after the rotation are congruent.
- **Statement 4: \( \angle E \cong \angle X \)**
- **False.** These angles are not congruent as \( E \) rotates to \( Y \), not \( X \).
The only statement that must be true after the rotation is:
**\( \angle F \cong \angle Z \)**
1. **Understanding the rotation:**
- A \( -90 \) degree clockwise rotation can be interpreted through the following point transformation:
- \( (x, y) \) becomes \( (y, -x) \).
- Therefore, the vertex relationships change as follows:
- Point \( E \) rotates to point \( Y \).
- Point \( F \) rotates to point \( Z \).
- Point \( G \) rotates to point \( X \).
2. **Analyzing the statements:**
- **Statement 1: \( \overline{EG} \cong \overline{XY} \)**
- **False.** Since \( G \) rotates to \( X \), this segment does not represent congruence.
- **Statement 2: \( \overline{EF} \cong \overline{XZ} \)**
- **False.** \( F \) goes to \( Z \) and does not support this congruence.
- **Statement 3: \( \angle F \cong \angle Z \)**
- **True.** Angles corresponding after the rotation are congruent.
- **Statement 4: \( \angle E \cong \angle X \)**
- **False.** These angles are not congruent as \( E \) rotates to \( Y \), not \( X \).
The only statement that must be true after the rotation is:
**\( \angle F \cong \angle Z \)**