TriangleEFG is rotated - 90 degrees (clockwise) to create triangleXYZ. which of the following statements must be true?

Question

A. ∠E ≅ ∠X
B. line EF ≅ line XZ
C. ∠F ≅ ∠Z
D. line EG ≅ line XY

Answer 1

When triangle EFG is rotated -90 degrees (clockwise) to create triangle XYZ, the following geometric properties hold true:

1. Corresponding angles are equal in measure.
2. Corresponding sides are equal in length.

Based on the provided options and knowing that a rotation does not change the sizes or measures of the original triangle:

• A. ∠E ≅ ∠X: This statement is true, as ∠E corresponds to ∠X after the rotation.

• B. line EF ≅ line XZ: This statement is not necessarily true, as line EF corresponds to line XY, not line XZ.

• C. ∠F ≅ ∠Z: This statement is true, as ∠F corresponds to ∠Z after the rotation.

• D. line EG ≅ line XY: This statement is true, as line EG corresponds to line XY after the rotation.

Therefore, the statements that must be true are:

• A. ∠E ≅ ∠X
• C. ∠F ≅ ∠Z
• D. line EG ≅ line XY

Thus, A, C, and D are correct. If you are required to choose only one statement that must be true, it can depend on the context in which the question was asked, but generally, A is a suitably correct answer.