Question

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

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. The order of the vertices in the triangle names gives the corresponding parts.

Step2: Identify corresponding parts

For \(\triangle EFG\) rotated to \(\triangle XYZ\), \(\angle E\) corresponds to \(\angle X\), \(\angle F\) corresponds to \(\angle Y\), \(\angle G\) corresponds to \(\angle Z\), \(EF\) corresponds to \(XY\), \(FG\) corresponds to \(YZ\), and \(EG\) corresponds to \(XZ\).

Answer:

\(\angle E\cong\angle X\)