1. the image is multiplied by the scale factor. if the scale factor is 2, the image is twice the size of the preimage. if the scale factor is ⅓, the image is one third the size. only a scale factor of 1 preserves congruency
Answer: If an image of a triangle is congruent to the pre-image, then the scale factor of the dilation must be n = <u> 1</u>.
Step-by-step explanation:
A dilation is a transformation that produces an image that is similar as the original, but has a different size. In a dilation, the corresponding the sides of the pre-image and sides of the image are proportional.
Let ΔPQR is dilated to ΔP'Q'R' such that ΔPQR≅ΔP'Q'R'
By CPCTC, PQ=P'Q' QR≅Q'R' and PR≅P'R'.
⇒ n=1
Hence, If an image of a triangle is congruent to the pre-image, then the scale factor of the dilation must be n = 1.