Final answer:
The question appears to contain typographical errors and lacks clear definitions or a diagram to provide a confident solution to prove congruency. An accurate depiction of the geometric problem is required in order to provide a detailed explanation or proof.
Step-by-step explanation:
It appears there is a typographical error in the question you have provided related to geometry, specifically concerning proving congruent segments or angles. Given the nature of such problems, typically the question would involve proving that certain lines are parallel and that this parallelism leads to congruent angles or segments due to the geometric properties of parallel lines and transversals.
For instance, if segments are designated by numbers, like segment 25, we would generally be asked to prove these segments are congruent based on given information such as corresponding angles being equal or alternate interior angles being congruent when two lines are cut by a transversal and those two lines are parallel.
However, without the correct notation or a diagram enabling a clear depiction of the geometric figures in question, it is impossible to confidently provide a solution to this problem. Please review and provide the correct notation for the question so that we can assist you further.