Question

△efg is rotated 90 degrees (clockwise) to create △xyz. which of the following statements must be true? (1 point)
∠f≅∠z
ef≅xz
∠e≅∠x
eg≅xy

Explanation:

Step1: Recall rotation property

A rotation is a rigid - motion transformation. Rigid - motion transformations preserve angle measures and side lengths. When $\triangle EFG$ is rotated to create $\triangle XYZ$, corresponding angles are congruent and corresponding sides are congruent.

Step2: Identify corresponding parts

The angle $\angle E$ in $\triangle EFG$ corresponds to the angle $\angle X$ in $\triangle XYZ$. Since rotation preserves angle - measure, $\angle E\cong\angle X$.

Step3: Analyze other options

For option A, $\angle F$ and $\angle Z$ are not corresponding angles. For option B, $EF$ and $XZ$ are not corresponding sides. For option D, $EG$ and $XY$ are not corresponding sides.

Answer:

C. $\angle E\cong\angle X$