It seems like you're trying to fill in the blanks with relevant terms related to a geometric theorem, possibly the congruence of triangles. Here’s a way to complete your sentences:
Given two triangles, you can show that a sequence of rigid transformations (such as translations, rotations, and reflections) will map one triangle onto the other triangle such that they overlap perfectly. This means that the corresponding sides and angles of the triangles are equal. Therefore, the Triangle Congruence Theorem is true.
If you had a specific theorem in mind or additional details, please let me know for more tailored help!