Question

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

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 angles and corresponding sides are congruent.

Step2: Identify corresponding parts

The corresponding parts of \(\triangle EFG\) and \(\triangle XYZ\) are determined by the rotation. The angle \(\angle E\) in \(\triangle EFG\) corresponds to the angle \(\angle X\) in \(\triangle XYZ\), \(\angle F\) corresponds to \(\angle Y\), \(\angle G\) corresponds to \(\angle Z\), \(\overline{EF}\) corresponds to \(\overline{XY}\), \(\overline{FG}\) corresponds to \(\overline{YZ}\), and \(\overline{EG}\) corresponds to \(\overline{XZ}\).

Answer:

D. \(\angle E\cong\angle X\)