To determine the scale factor of the dilation when an image of a triangle is congruent to its pre-image, we need to understand the concept of congruence and dilation in geometry.
Congruence: When two figures are congruent, they have the same shape and size. All corresponding angles and sides are equal in measurement.
Dilation: Dilation is a transformation that changes the size of a figure but not its shape. The scale factor of dilation describes how much the figure is stretched or compressed. If the scale factor is greater than 1, the figure is enlarged. If the scale factor is between 0 and 1, the figure is reduced in size.
Given that the image of the triangle is congruent to its pre-image, there is neither an enlargement nor reduction of the triangle. Essentially, the size of the image remains exactly the same as the pre-image. For dilation to maintain the same size, the scale factor must be 1. This is because multiplying by 1 leaves the dimensions unchanged.
Thus, if an image of a triangle is congruent to the pre-image, the scale factor of the dilation is:
1
Hence, the correct answer is:
1
