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

∠F≅∠Z
angle upper F congruent to angle upper Z

EF¯¯¯¯¯¯¯¯≅XZ¯¯¯¯¯¯¯¯
Modifying above upper E upper F with bar congruent to Modifying above upper X upper Z with bar

∠E≅∠X
angle upper E congruent to angle upper X

Answer 1

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 \( \triangle XYZ \).

1. **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 \( \triangle XYZ \).

2. **∠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 \( \triangle XYZ \).

3. **EF ≅ XZ**: Similar to the first case, this statement is true. During the rotation, side \( \overline{EF} \) remains congruent to side \( \overline{XZ} \).

4. **∠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.