Which pair of transformations could map triangleABC to triangle A’B’C such that the triangles are smaller but not congruent

Answer 1

To map triangle ABC to triangle A’B’C such that the triangles are smaller but not congruent, you can use a combination of the following transformations:

1. Reduction (Scale Down): Apply a dilation transformation with a scale factor less than 1 (e.g., 0 < k < 1) centered at a point (which could be the centroid of triangle ABC, or any other point). This transformation will shrink triangle ABC uniformly in all directions, resulting in a smaller triangle. This will reduce the size of the triangle but still maintain the shape, meaning the smaller triangle A’B’C is similar to triangle ABC, but not congruent (since they have different sizes).

2. Rotation or Reflection: After dilation, you can apply a rotation or reflection to reposition the smaller triangle A’B’C in a way that it is not in the same orientation or mirror position as triangle ABC. This would ensure that the final triangle A’B’C looks different in orientation compared to the original triangle ABC.

Using these two transformations together—first scaling down and then applying a rotation or reflection—will successfully map triangle ABC to triangle A’B’C, resulting in triangles that are similar but not congruent.