Question

c. how can you be sure your image shows an accurate reduction? select the correct phrases to complete each sentence. the image has angle measures as the preimage. the side lengths are as the preimage.

Explanation:

For a reduction (a type of similarity transformation, like dilation with a scale factor less than 1), the properties of similar figures apply. Similar figures have equal (congruent) angle measures, and their corresponding side lengths are proportional (specifically, scaled by the same factor, so for a reduction, the side lengths of the image are shorter but in proportion, or "a fraction" / "proportional" with a scale factor <1). So the first blank should be "the same" (since angle measures are preserved in similarity transformations like dilation) and the second blank should be "proportional (or a fraction of, e.g., shorter but in proportion)" but in the context of typical fill - ins for reduction (similarity), the first is "the same" and the second is "a fraction (or proportional, scaled by a factor <1)". Commonly, for the first sentence: "The image has the same angle measures as the preimage." For the second: "The side lengths are a fraction (or proportional, e.g., shorter in proportion) as the preimage." (If options were like "the same", "different"; "proportional (shorter)", "equal" etc., the correct ones are "the same" for angles (since dilation preserves angle measure) and "proportional (or a fraction of, i.e., smaller in proportion)" for side lengths (since reduction is a dilation with scale factor <1, so sides are scaled by that factor, hence proportional and shorter).)

Answer:

The image has \boxed{the same} angle measures as the preimage.
The side lengths are \boxed{a fraction (or proportional, e.g., shorter in proportion)} as the preimage.

(Note: If the dropdown options for the second blank were something like "proportional (shorter)" or "scaled by a factor less than 1" or "a fraction of the length", the exact wording would match the options. But based on the general concept of reduction (similarity), angles are same, sides are proportional (shorter in proportion).)