Question
△EFG is rotated −90 degrees (clockwise) to create △XYZ . Which of the following statements must be true?(1 point)Responses∠F≅∠Z angle upper F congruent to angle upper Z∠E≅∠X angle upper E congruent to angle upper XEF¯¯¯¯¯¯¯¯≅XZ¯¯¯¯¯¯¯¯Modifying above upper E upper F with bar congruent to Modifying above upper X upper Z with barEG¯¯¯¯¯¯¯¯≅XY¯¯¯¯¯¯¯¯
Answers
Answered by
GPT-4o mini
To determine which statements must be true after triangle \( \triangle EFG \) is rotated -90 degrees (clockwise) to create triangle \( \triangle XYZ \), we need to analyze the transformation that occurs with the rotation.
When a triangle is rotated -90 degrees (clockwise), the following properties hold for the angles and sides:
1. The angles remain congruent. Therefore,
- \( \angle F \) corresponds to \( \angle Z \), meaning \( \angle F \cong \angle Z \).
- \( \angle E \) corresponds to \( \angle X \), so \( \angle E \cong \angle X \).
- \( \angle G \) corresponds to \( \angle Y \), hence \( \angle G \cong \angle Y \).
2. The congruence of sides will also hold. Thus:
- The length of segment \( EF \) will correspond to the length of segment \( XZ \): \( EF \cong XZ \).
- The length of segment \( EG \) corresponds to the length of segment \( XY \): \( EG \cong XY \).
- The length of segment \( FG \) corresponds to the length of segment \( YZ \): \( FG \cong YZ \).
Based on the properties of rotation, the following statements must be true:
1. \( \angle F \cong \angle Z \)
2. \( \angle E \cong \angle X \)
3. \( EF \cong XZ \)
4. \( EG \cong XY \)
Therefore, all the statements about the angles and the side lengths outlined in the question (as they appear) must be true after the rotation.
To specifically identify which of the provided responses must be true, we can summarize:
- \( \angle F \cong \angle Z \) is true.
- \( \angle E \cong \angle X \) is true.
- \( EF \cong XZ \) is true.
- \( EG \cong XY \) is true.
Therefore, all statements regarding the congruence of angles and corresponding sides after the rotation hold true based on the laws of geometry.
When a triangle is rotated -90 degrees (clockwise), the following properties hold for the angles and sides:
1. The angles remain congruent. Therefore,
- \( \angle F \) corresponds to \( \angle Z \), meaning \( \angle F \cong \angle Z \).
- \( \angle E \) corresponds to \( \angle X \), so \( \angle E \cong \angle X \).
- \( \angle G \) corresponds to \( \angle Y \), hence \( \angle G \cong \angle Y \).
2. The congruence of sides will also hold. Thus:
- The length of segment \( EF \) will correspond to the length of segment \( XZ \): \( EF \cong XZ \).
- The length of segment \( EG \) corresponds to the length of segment \( XY \): \( EG \cong XY \).
- The length of segment \( FG \) corresponds to the length of segment \( YZ \): \( FG \cong YZ \).
Based on the properties of rotation, the following statements must be true:
1. \( \angle F \cong \angle Z \)
2. \( \angle E \cong \angle X \)
3. \( EF \cong XZ \)
4. \( EG \cong XY \)
Therefore, all the statements about the angles and the side lengths outlined in the question (as they appear) must be true after the rotation.
To specifically identify which of the provided responses must be true, we can summarize:
- \( \angle F \cong \angle Z \) is true.
- \( \angle E \cong \angle X \) is true.
- \( EF \cong XZ \) is true.
- \( EG \cong XY \) is true.
Therefore, all statements regarding the congruence of angles and corresponding sides after the rotation hold true based on the laws of geometry.