Answer:
As congruent shapes are always similar, all the given sequences of transformations will result in an image that is similar to its pre-image.
However, if you are looking for a sequence of transformations that is similar and non-congruent, then this would be "A reflection followed by a dilation".
Step-by-step explanation:
Translation: A translation moves an object left, right, up or down. Every point on the original object is translated (moved) the same distance in the same direction.
Rotation: An object is rotated around a center. The distance from any point on the object to the center stays the same.
Reflection: An object can be reflected across a line of reflection. Every point on the reflected object is the same distance from the line of reflection as the corresponding points on the original object.
Dilation: Dilation changes the size of an object without changing its shape. The size of the object may be increased or decreased based on the scale factor.
Congruent shapes have the same area, size, angles and lengths as each other. If the image can be rotated, reflected or translated to fit exactly onto the pre-image, then the shapes are said to be congruent.
If a shape is dilated, then the shapes are said to be similar. Similar shapes are not the same size as each other but their corresponding sides of are in the same proportion and their corresponding angles are congruent.
Congruent shapes are always similar. Therefore, all the given sequences of transformations result in an image that is similar to its pre-image.
