Final answer:
The squares t and t³ are similar because translations preserve shape and size while dilations scale shapes proportionally, preserving the angles. The corresponding angles in both squares are congruent and their sides are proportional, making statement 2 the correct answer.
Step-by-step explanation:
The square t was translated by the rule (x + 2, y + 2) and then dilated from the origin by a scale factor of 3 to create square t³. To understand why the squares are similar, we should know that translations and dilations are two types of geometric transformations. A translation slides a shape on the plane without altering its size or shape, while a dilation scales a shape larger or smaller, but keeps its shape proportional. The statement that explains why the squares are similar is: Translations and dilations preserve collinearity; therefore, the corresponding angles of squares t and t³ are congruent. This is because translations do not change angles or shapes at all and dilations scale all distances by the same factor, so the angles remain the same. While translations do not affect size and therefore do not preserve side length directly, dilations do and the side lengths of t³ would be 3 times those of t. Therefore, the correct answer is statement 2, which encompasses the fact that both translations and dilations preserve the angles, and the sides are proportional due to dilation by a scale factor.