To determine the scale factor of a dilation, we need to examine the relationship between the original shape (pre-image) and its transformed shape (image).
A dilation is a transformation that changes the size of a figure, but not its shape. The scale factor of the dilation is the ratio of any side length of the image to the corresponding side length of the pre-image.
If the image of a triangle is congruent to the pre-image, this means that the image and the pre-image are exactly the same in size and shape. Congruent figures have corresponding sides of the same length and corresponding angles of the same measure.
Since the two triangles are congruent, their side lengths are identical. Therefore, the scale factor must be such that each side length of the image is equal to the corresponding side length of the pre-image.
This condition is met when the scale factor is 1 because multiplying any side length by 1 leaves the length unchanged.
In conclusion, the scale factor of the dilation when the image is congruent to the pre-image is:
[tex]\[ \boxed{1} \][/tex]
