A.) The lengths of the sides and the measures of the angles are preserved, so the triangles are congruent.
It's easier to demonstrate this instead of using math. Take a piece of graph paper and draw an X and Y axis on it. Then take a sheet of clear plastic and place that over the graph paper. Now draw a triangle on that piece of plastic. Now, push a pin through the plastic and through the origin on the graph paper. Finally, rotate the sheet of plastic around the pin to various angles. Does the shape of the drawn triangle ever change, regardless of how much or little you rotate it? The answer is "no". No matter what the rotation, the image and pre-image if the triangle remains congruent.
