Final answer:
Yes, polygons can be similar if they have the same shape but different sizes. Two polygons are similar if their corresponding angles are congruent and their corresponding side lengths are proportional. The scale factor is the ratio of corresponding side lengths.
Step-by-step explanation:
Yes, polygons can be similar if they have the same shape but different sizes. Two polygons are similar if their corresponding angles are congruent and their corresponding side lengths are proportional. To write a similarity statement, we can use the corresponding angles and side lengths.
For example, if we have two polygons, ABCD and EFGH, and angle A is congruent to angle E, angle B is congruent to angle F, angle C is congruent to angle G, and angle D is congruent to angle H, then we can write the similarity statement as ABCD ~ EFGH.
The scale factor is the ratio of corresponding side lengths. We can calculate the scale factor by comparing the lengths of corresponding sides. If one side of polygon ABCD is 5 units long and the corresponding side of polygon EFGH is 10 units long, then the scale factor is 10/5 = 2. So, the scale factor is 2.