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?

1) Triangles SRT and YXZ verify segment SR ≅ segment YX and segment ST ≅ segment YZ by translation. Verify ∠S ≅ ∠Y and ∠T ≅ ∠Z by reflection.
2) Triangles SRT and YXZ verify segment SR ≅ segment YX and segment ST ≅ segment YZ by reflection. Verify ∠S ≅ ∠Y and ∠T ≅ ∠Z by translation.
3) Triangles SRT and YXZ verify segment SR ≅ segment YX and segment ST ≅ segment YZ by reflection. Verify ∠S ≅ ∠Y and ∠T ≅ ∠Z by reflection.
4) Triangles SRT and YXZ verify segment SR ≅ segment YX and segment ST ≅ segment YZ by translation. Verify ∠S ≅ ∠Y and ∠T ≅ ∠Z by translation.

Answer 1

The toy maker can confirm similarity by verifying segment congruence and angle congruence using either translation or reflection.

Step-by-step explanation:

The toy maker can confirm that the pieces are similar using the definition of similarity in terms of similarity transformations by performing translation and reflection on the corresponding parts of the triangles.

1. For translation, the toy maker should verify that segment SR is congruent to segment YX and segment ST is congruent to segment YZ.
2. For reflection, the toy maker should verify that angle S is congruent to angle Y and angle T is congruent to angle Z.
3. To confirm similarity, both segment congruence and angle congruence must be satisfied using one approach, either translation or reflection.