Question

Why do you think the parallel sides in figure GHIJ remain parallel to the corresponding sides of figure G'H'IJ' after the dilation?

Answer 1

we know that

The dilation is a non rigid trabsformation

That means

The dilation produces similar figures

If two figures are similar, then the ratio of its corresponding sides is proportional and its corresponding angles are congruent

so

figure GHIJ remain parallel to the corresponding sides of figure G'H'IJ' after the dilation