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?

A) ΔABC ~ ΔDEF because of the definition of similarity in terms of similarity transformations.

B) Segment BC ~ Segment DE because of the AA similarity postulate.

C) ΔABC ~ ΔDEF because of the AA similarity postulate.

D) Segment BC ~ Segment DE because of the definition of similarity in terms of similarity transformations.

Answer 1

The statement that is true is Segment BC ~ Segment DE because of the definition of similarity in terms of similarity transformations.

Step-by-step explanation:

If a series of rigid transformations maps ∠F onto ∠C where ∠F is congruent to ∠C, then the statement that is true is D) Segment BC ~ Segment DE because of the definition of similarity in terms of similarity transformations.

In geometry, similar figures have corresponding angles that are congruent and corresponding sides that are proportional. Since the angles ∠F and ∠C are congruent and have been mapped onto each other through rigid transformations, it means that the corresponding sides BC and DE are also proportional and therefore Segment BC is similar to Segment DE.