Answer:
In order to find the scale factor of ABCD to EFGH, we need to find the ratio of corresponding side lengths of the two similar figures.
Let's assume that ABCD and EFGH are similar quadrilaterals. We can label the side lengths of ABCD as AB = a, BC = b, CD = c, and DA = d, and the side lengths of EFGH as EF = w, FG = x, GH = y, and HE = z.
The scale factor k is defined as the ratio of corresponding side lengths, such that k = EF/AB = FG/BC = GH/CD = HE/DA.
Therefore, to find the scale factor, we can choose any pair of corresponding sides and divide their lengths. For example, we can choose AB and EF, and get:
k = EF/AB = w/a
Similarly, we can choose other corresponding sides and get:
k = FG/BC = x/b
k = GH/CD = y/c
k = HE/DA = z/d
Since ABCD and EFGH are similar, all four ratios must be equal, so we can set them equal to each other:
w/a = x/b = y/c = z/d
This equation tells us that the scale factor is the same for all corresponding sides of the two quadrilaterals. Therefore, we can find the scale factor by choosing any two corresponding sides and dividing their lengths.