Question

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

Explanation:

Step1: Understand similarity transformations

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

Step2: Analyze Polygon 2 and Polygon 4

• Count the grid units for corresponding sides.
• For Polygon 2: Let's assume some side lengths. For example, if we consider the vertical and horizontal segments (after analyzing the shape).
• For Polygon 4: We can observe that the angles of Polygon 2 and Polygon 4 are the same (by visual inspection of the shape of the polygons, as they have the same number of sides and the "bend" angles look congruent).
• Also, the ratio of their corresponding side lengths is constant. If we assume a side length of Polygon 2 as \(x\) (counted in grid units) and the corresponding side length of Polygon 4 as \(y\), we can find that \(\frac{y}{x}\) is a constant value (by counting the number of grid units for multiple corresponding sides).

Answer:

C. polygons 2 and 4