Bot GPT 4-o mini When triangle \( \triangle EFG \) is rotated \( -90 \) degrees (clockwise), we can analyze the relationships between the sides and angles of the original triangle and the rotated triangle \( \triangle XYZ \).
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EG ≅ XY: This statement is true. When a triangle is rotated, the lengths of the sides remain the same. Thus, side \( \overline{EG} \) of triangle \( \triangle EFG \) will be congruent to side \( \overline{XY} \) of triangle \( \triangle XYZ \).
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∠F ≅ ∠Z: This statement is also true. When a triangle is rotated, the angles also remain the same, so \( \angle F \) in triangle \( \triangle EFG \) will be congruent to angle \( \angle Z \) in triangle \( \triangle XYZ \).
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EF ≅ XZ: Similar to the first case, this statement is true. During the rotation, side \( \overline{EF} \) remains congruent to side \( \overline{XZ} \).
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∠E ≅ ∠X: This statement is true as well. The angles of the triangle remain congruent after rotation, so angle \( \angle E \) in triangle \( \triangle EFG \) will be congruent to angle \( \angle X \) in triangle \( \triangle XYZ \).
Therefore, all of the statements given must be true regarding the properties of triangles before and after rotation.
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