Final answer:
A rhombus and a square can be mapped onto each other by similarity transformations because a square is a special case of a rhombus with all sides equal, and hence they can have the same shape with proportional sides.
Step-by-step explanation:
The question is asking which polygons can be mapped onto each other by similarity transformations. A similarity transformation includes scaling (enlarging or reducing), translation (sliding), rotation, and reflection. For two polygons to be similar, they must have the same shape but not necessarily the same size. This means that their corresponding angles are equal and their corresponding sides are proportional.
Now, let's look at the options given:
- A Rhombus and Square: These two shapes can be similar as all squares are rhombuses (with all angles being 90 degrees), but not all rhombuses are squares. So, a square can be seen as a rhombus with equal sides, meaning they can be mapped onto each other by similarity transformations.
- B Pentagon and Hexagon: They cannot be similar because they have a different number of sides.
- C Rectangle and Trapezoid: They cannot be similar because a trapezoid has only one pair of parallel sides, whereas a rectangle has two pairs of parallel sides.
- D Equilateral Triangle and Scalene Triangle: They cannot be similar because all sides and angles in an equilateral triangle are the same, but in a scalene triangle, no sides or angles are equal.
Therefore, the correct answer is A. A Rhombus and Square can be mapped onto each other by similarity transformations.