## Elementary Geometry for College Students (6th Edition)

Both parallelograms ABCD and DCFE are similar because the two conditions of similarity satisfied. 1- corresponding angles are congruent since segment $AB\parallel DC \parallel EF$. 2- sides are proportional to each other $\frac{AD}{DE}=\frac{BC}{CF}=\frac{AB}{DC}=1$ Noting that, since the two transversals are parallel then by theorem the distance between any two parallel lines is the same. Therefore AB= DC = EF.