Question

the abc toy company is creating two similar pieces for a board game, as shown. how could the toy maker confirm that the pieces are similar using the given information? verify ∠a≅∠d and ∠b≅∠e by translation. verify (overline{ab}congoverline{de}) and (overline{bc}congoverline{ef}) by translation. verify ∠a≅∠d and ∠b≅∠e by reflection. verify (overline{ab}congoverline{de}) and (overline{bc}congoverline{ef}) by reflection.

Explanation:

Step1: Recall similarity criterion

Two triangles are similar if their corresponding angles are congruent. Translating or reflecting triangles does not change the angle - measures. Verifying $\angle A\cong\angle D$ and $\angle B\cong\angle E$ would help confirm similarity as per the AA (angle - angle) similarity criterion.

Step2: Analyze side - length verification

Verifying side - lengths being congruent ($\overline{AB}\cong\overline{DE}$ and $\overline{BC}\cong\overline{EF}$) by translation or reflection only shows congruence of the sides, not similarity of the triangles. Similarity is about proportional sides and equal angles.

Answer:

Verify $\angle A\cong\angle D$ and $\angle B\cong\angle E$ by translation.