Question

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

EG≅XY
EF≅XZ
∠F≅∠Z
∠E≅∠X

what is correct

Answer 1

To determine which statements must be true after the rotation of triangle \( \triangle EFG \) by \(-90\) degrees (clockwise) to create triangle \( \triangle XYZ \), let's analyze the transformation.

When a triangle is rotated \( -90 \) degrees (clockwise), the vertices will change position in the following way:

1. The vertex that was at \( E \) will move to the position where \( X \) is.
2. The vertex that was at \( F \) will move to the position where \( Y \) is.
3. The vertex that was at \( G \) will move to the position where \( Z \) is.

Thus, the new corresponding vertices are:
- \( E \) corresponds to \( X \)
- \( F \) corresponds to \( Y \)
- \( G \) corresponds to \( Z \)

Now we can evaluate the statements:

1. **EG ≅ XY** - This statement cannot be guaranteed after the rotation, as it pertains to the sides, which may or may not correspond exactly post-rotation.

2. **EF ≅ XZ** - This statement is also not necessarily true for the same reasons as above; the side lengths correspond to different vertices.

3. **∠F ≅ ∠Z** - Since the angles maintain their relationships through rotation, this statement is true.

4. **∠E ≅ ∠X** - Similarly, this statement is also true, as angle \( E \) rotates into angle \( X \).

Based on the analysis:
- The statements that must be true after the rotation are **∠F ≅ ∠Z** and **∠E ≅ ∠X**.

If the question allows for selecting true statements, then both the statements about angles must be correct.