Question

if a series of rigid transformations maps ∠f onto ∠c where ∠f is congruent to ∠c, then which of the following statements is true? △abc ~ △fde because of the definition of similarity in terms of similarity transformations △abc ~ △fde because of the aa similarity postulate (overline{bc}) ~ (overline{ef}) because of the definition of similarity in terms of similarity transformations (overline{bc}) ~ (overline{ef}) because corresponding parts of similar triangles are proportional

Explanation:

Step1: Analyze the given angles

We know that \(\angle A=\angle D = 90^{\circ}\) (right - angles) and \(\angle F=\angle C\) (given).

Step2: Apply the AA (Angle - Angle) similarity postulate

The AA similarity postulate states that if two angles of one triangle are congruent to two angles of another triangle, then the two triangles are similar.
For \(\triangle ABC\) and \(\triangle FDE\), we have two pairs of congruent angles (\(\angle A\cong\angle D\) and \(\angle C\cong\angle F\)).

Answer:

\(\triangle ABC\sim\triangle FDE\) because of the AA similarity postulate.