To determine the scale factor of dilation when the image of a triangle is congruent to the pre-image, we need to understand the properties of congruent figures.
Two figures are congruent if they have the same size and shape. This implies that all corresponding angles and sides in the two figures are equal. When we perform a dilation on a figure, we either enlarge or reduce it by a certain scale factor.
The scale factor of a dilation is the ratio of any side length of the image to the corresponding side length of the pre-image. In the case of congruent figures, since the image has the same size and shape as the pre-image, the lengths of corresponding sides are equal.
Therefore, the scale factor that preserves the size and shape (maintains congruence) is 1. This means each side of the triangle image is exactly the same length as the corresponding side of the original triangle.
Thus, the scale factor of the dilation is:
[tex]\[ \boxed{1} \][/tex]
