Question

which polygons can be mapped onto each other by similarity transformations?
a. polygons 1 and 2
b. polygons 1 and 4
c. polygons 1 and 3
d. polygons 2 and 4

Explanation:

Step1: Understand similarity transformations

Similarity transformations include rotations, reflections, translations, and dilations. Similar polygons have the same shape (corresponding angles are equal) and their side - lengths are in proportion.

Step2: Analyze the polygons

• Polygons 2 and 4:
• By visual inspection (or if we assume we can calculate the ratios of corresponding side - lengths if we had coordinate - based side - length formulas \(d=\sqrt{(x_2 - x_1)^2+(y_2 - y_1)^2}\)).
• The general shape of Polygon 2 and Polygon 4 is the same. If we consider the concept of similarity (same number of sides, angles match in terms of measure), we can assume that a dilation (a type of similarity transformation) can map one onto the other.
• Polygon 1 has a different number of sides (it is a pentagon with a different angular structure compared to 2 and 4). Polygon 3 also has a different angular and side - length proportion compared to 1, 2, and 4.

Answer:

D. polygons 2 and 4