Question

△efg is rotated - 90 degrees (clockwise) to create △xyz. which of the following statements must be true? (1 point)
○ (overline{eg}congoverline{xy})
○ (overline{ef}congoverline{xz})
○ (angle econgangle x)
○ (angle fcongangle z)

Explanation:

Step1: Recall rotation property

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

Step2: Identify corresponding parts

The vertices of $\triangle EFG$ and $\triangle XYZ$ are related by the rotation. The corresponding vertices are $E$ and $X$, $F$ and $Y$, $G$ and $Z$. Corresponding angles are congruent. So, $\angle E\cong\angle X$, $\angle F\cong\angle Y$, $\angle G\cong\angle Z$. Also, $\overline{EF}\cong\overline{XY}$, $\overline{FG}\cong\overline{YZ}$, $\overline{EG}\cong\overline{XZ}$.

Answer:

$\angle E\cong\angle X$