When triangle EFG is rotated -90 degrees (clockwise) to create triangle XYZ, the following characteristics about the triangles hold true:
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Congruent Sides: The sides of triangle EFG will correspond to the sides of triangle XYZ. This means that each side of the original triangle is congruent to a corresponding side of the rotated triangle.
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Corresponding Angles: The angles of triangle EFG will correspond to the angles of triangle XYZ.
Given this, let's analyze the statements:
A. EF ≌ XZ - This statement must be true because under rotation, corresponding sides remain congruent.
B. ∠F ≌ ∠Z - This statement must be true as the angles in a triangle remain the same under rotation.
C. ∠E ≌ ∠X - This statement must also be true for the same reason as B - the corresponding angles remain congruent.
D. EG ≌ XY - This statement must be true since the sides correspond and remain the same length after rotation.
In conclusion, all statements (A, B, C, D) are true given the rotation implies correspondence between the respective sides and angles of the triangles involved. If the question provides a prompt stating that "which of the following statements must be true?" typically implies identifying those statements will rely on properties of congruence and characteristics of geometric transformations like rotations.
Thus, all the given statements (A, B, C, D) must be true if △EFG is rotated -90 degrees (clockwise) to create △XYZ.
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