Which two transformations are applied to pentagon abcde to create a'b'c'd'e'?

Translation, Rotation and Reflection.

Step-by-step explanation:

First note that P_1=ABCDE and P_2=A'B'C'D'E' are congruent pentagons, then the transformarion that we use to send P_1 to P_2 must preserve distances, which means that we only can use translatons, rotations and reflections. We first use the translation  that sents C to C' to send P_1 to a pentagon P_3 that only shares shares the vertex C' with P_2, let D'' be the image of the vertex D under the translation, the distances of the segments CD, C'D' and C'D'' are the same. Therefore, we might use a rotation that sends C'D'' to C'D', this rotation to sends the pentagon P_3  to a pentagon P_4 that shares the side C'D' with P_2 and that its coungruent to both P_1=ABCDE and P_2=A'B'C'D'E'. Finaly, we might reflect P_4 across the line that goes trhough C'D' and so P_4 wil be send to P_2=A'B'C'D'E'.

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Step-by-step explanation: