Question

the abc toy company is creating two similar pieces for a board game, as shown below. how could the toy maker confirm that the pieces are similar using the definition of similarity in terms of similarity transformations? verify $overline{sr}congoverline{yx}$ and $overline{st}congoverline{yz}$ by translation. verify $angle scongangle y$ and $angle tcongangle z$ by reflection. verify $overline{sr}congoverline{yx}$ and $overline{st}congoverline{yz}$ by reflection. verify $angle scongangle y$ and $angle tcongangle z$ by translation.

Explanation:

Step1: Recall similarity - transformation definition

Two figures are similar if one can be obtained from the other by a sequence of translations, rotations, reflections, and dilations. For two triangles to be similar, corresponding angles must be congruent.

Step2: Analyze each option

• Option 1: Verifying side - congruence by translation does not confirm similarity. Similarity is about angle - congruence and proportional side - lengths, not just side - congruence.
• Option 2: Verifying $\angle S\cong\angle Y$ and $\angle T\cong\angle Z$ by reflection is correct. If we can map the angles of one triangle to the angles of the other triangle through a reflection (and we can also consider other similarity - transformations), and show that all corresponding angles are congruent, we can confirm similarity.
• Option 3: Verifying side - congruence by reflection does not confirm similarity.
• Option 4: Verifying angle - congruence by translation is not the key way to confirm similarity. The main idea is to show that corresponding angles are congruent through similarity - transformations.

Answer:

Verify $\angle S\cong\angle Y$ and $\angle T\cong\angle Z$ by reflection.