Final answer:
The statement that must be true is A) A figure and its dilation must be similar, as dilations produce figures with proportional sides and corresponding angles that are congruent, regardless of the size change. The other statements are incorrect as a dilation can produce a smaller figure and such figures are not congruent, only similar.
Step-by-step explanation:
The question presented is asking which statement about dilations must be true, offering four options as potential statements. The correct answer is:
A) A figure and its dilation must be similar.
This statement is always true because dilations produce figures with all corresponding angles congruent and the sides are proportional to each other, which is the definition of similar figures. The other options B, C and D have false elements because:
- B) A dilation does not necessarily have to be larger; it can also be smaller if the scale factor is less than 1.
- C) Congruent figures are the same shape and size, but a dilation changes the size, so the figures won't be congruent unless the scale factor is 1.
- D) The ratio of corresponding sides could also be less than 1 if the figure is reduced in size through the dilation.