Write a series of rigid motions that transform pentagon ABCDE to pentagon A′B′C′D′E′.
To determine the series of rigid motions that can transform pentagon ABCDE to pentagon A'B'C'D'E', we can use a combination of translations, rotations, and reflections.
1. Translation: Move point A to the corresponding point A' using a translation vector. Any vector AB' or AE' can be used to translate A to A'. The translation vector will be the same for all points.
2. Rotation: Once point A has been translated to A', we can rotate the remaining points such that AB is parallel to A'B'. Choose any of the remaining four points, for example point B, and find the angle between lines AB and A'B'. Rotate points B, C, D, and E around point A' by this angle to align AB with A'B'.
3. Reflection: After the translation and rotation steps, the pentagons will be in the same position and orientation, but they might be facing opposite directions. We can use a reflection to align the remaining points C, D, and E with the corresponding points C', D', and E'. Reflect the remaining points about the line that connects points A' and B'.
By following these three steps - translation, rotation, and reflection - we can transform pentagon ABCDE to pentagon A'B'C'D'E'.