Question

△EFG
is rotated −90
degrees (clockwise) to create △XYZ
. Which of the following statements must be true?(1 point)
Responses

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

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¯¯¯¯¯¯¯¯

Answer 1

When a triangle is rotated \(-90\) degrees clockwise, the following relationships hold true for the angles and sides of the triangle:

1. **Angles**: The angles of the original triangle correspond to those of the new triangle in a specific order determined by the rotation. For triangle \(EFG\) that is rotated to form triangle \(XYZ\):
- \(\angle E\) corresponds to \(\angle X\)
- \(\angle F\) corresponds to \(\angle Z\)
- \(\angle G\) corresponds to \(\angle Y\)

2. **Sides**: The sides of the original triangle also correspond to the sides of the new triangle in the same order. Thus:
- \(EG\) corresponds to \(XY\)
- \(EF\) corresponds to \(XZ\)
- \(FG\) corresponds to \(YZ\)

Considering these relationships, the true statements resulting from the rotation are as follows:

1. \(\angle E \cong \angle X\) (This statement must be true)
2. \(EG \cong XY\) (This statement must be true)
3. \(\angle F \cong \angle Z\) (This statement must be true)
4. \(EF \cong XZ\) (This statement must be true)

All the given responses (1-4) are true because they follow directly from the properties of rotation.

To summarize:

- **True statements**:
- \(\angle E \cong \angle X\)
- \(EG \cong XY\)
- \(\angle F \cong \angle Z\)
- \(EF \cong XZ\)

Thus, each statement can be accepted as true due to the properties of the rotation.