The approach is to take advantage of the definition of a perpendicular bisector to show the base lengths and right angles are congruent, then use SAS with the second side being CD (congruent to itself). It's mainly a matter of deciding what the various reasons are called.
It seems the goal is to show that AC = BC as marked.
The image would coincide with the pre-image during the rotation. Therefore, the octagon would coincide a total of 8 times as it rotates 360 degrees about its center.
