Answer:
If a dilation is applied to a triangle, then the image must be similar.
Step-by-step explanation:
We have been given an incomplete sentence. We are supposed to fill in the given blank.
Sentence:
If a dilation is applied to a triangle, then the image must be _____.
Since we know that after dilating a figure by a scale factor, the resulting image will be either bigger or smaller than the original figure depending on the scale factor.
If the scale factor is greater than one, so resulting figure will be bigger than the original figure.
If the scale factor is less than one, so resulting figure will be smaller than the original figure.
Since all the angles of a triangle add up-to 180 degrees, so the measure of angles of the resulting figure will be same as the original triangle.
Since the corresponding sides of pre-image and image are proportional, so both triangles will be similar not congruent.
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