When dealing with transformations in geometry, particularly dilations, the scale factor determines how much a figure is enlarged or reduced. A dilation transformation changes the size of a figure, but not its shape.
In the specific case where the image of a triangle is congruent to the pre-image, this means that the two triangles have the same size and shape. Congruence implies that corresponding sides and angles of the triangle are exactly equal.
The scale factor in a dilation is defined as follows:
- A scale factor greater than 1 indicates an enlargement.
- A scale factor less than 1 (but greater than 0) indicates a reduction.
- A scale factor of 1 means that the size of the figure remains unchanged.
Since the image of the triangle is congruent to the pre-image, we conclude that there was no change in size. Therefore, the scale factor must be 1.
So, the answer to the question "If an image of a triangle is congruent to the pre-image, what is the scale factor of the dilation?" is:
[tex]\[
1
\][/tex]
