Question

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

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

EG¯¯¯¯¯¯¯¯≅XY¯¯¯¯¯¯¯¯
Modifying above upper E upper G with bar congruent to Modifying above upper X upper Y with bar

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

∠F≅∠Z

Answer 1

To analyze the rotation of triangle \( \triangle EFG \) by \( -90 \) degrees (clockwise) to form triangle \( \triangle XYZ \), we can use the properties of rotation transformations. Here are the results of that rotation:

1. **The point layout after rotation**:
- Point \( E \) will move to point \( Z \).
- Point \( F \) will move to point \( X \).
- Point \( G \) will move to point \( Y \).

2. **Congruent sides**:
Because the triangles are derived through a rigid motion (rotation), the corresponding sides will be congruent. Thus:
- \( \overline{EF} \cong \overline{XZ} \)
- \( \overline{EG} \cong \overline{XY} \)
- \( \overline{FG} \cong \overline{YZ} \)

3. **Congruent angles**:
The angles will also be congruent due to the nature of rotation:
- \( \angle E \cong \angle X \)
- \( \angle F \cong \angle Z \)
- \( \angle G \cong \angle Y \)

Given this analysis, the statements that must be true upon rotating triangle \( \triangle EFG \) by \( -90 \) degrees to create triangle \( \triangle XYZ \) would be:

1. **EF¯¯¯¯¯¯¯¯≅XZ¯¯¯¯¯¯¯¯** - This statement is true.
2. **EG¯¯¯¯¯¯¯¯≅XY¯¯¯¯¯¯¯¯** - This statement is true.
3. **∠E≅∠X** - This statement is true.
4. **∠F≅∠Z** - This statement is also true.

All statements listed are true after the rotation of the triangle.