△EFG

Question

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

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

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

EG¯¯¯¯¯¯¯¯≅XY¯¯¯¯¯¯¯¯

Answer 1

When a triangle (like triangle EFG) is rotated -90 degrees (or 90 degrees clockwise), the following transformations occur:

1. The orientation of the triangle changes.
2. The lengths of the sides remain congruent.
3. The original angles remain congruent.

To analyze your statements based on a -90 degree rotation:

1. EF̅̅̅̅̅̅ ≅ XZ̅̅̅̅̅̅: This statement is true because EF and XZ are the corresponding sides of the triangles before and after rotation.

2. ∠F ≅ ∠Z: This statement is true because angles F and Z correspond to each other after the -90 degree rotation.

3. ∠E ≅ ∠X: This statement is also true as angles E and X are corresponding angles after the rotation.

4. EG̅̅̅̅̅̅ ≅ XY̅̅̅̅̅̅: This statement is true because EG and XY are the corresponding sides of the triangles before and after rotation.

Given this analysis, all four statements must be true after the -90 degree rotation of triangle EFG to create triangle XYZ.