1. The problem involves proving congruence relationships between geometric figures, specifically given $\overline{CE} \cong \overline{UW}$ and $\angle C \cong \angle U$. 2. From the notation, $\overline{CE} \cong \overline{UW}$ means the line segments CE and UW are congruent, i.e., $|CE| = |UW|$. 3. Similarly, $\angle C \cong \angle U$ means that angle C is congruent to angle U, i.e., they have the same measure. 4. Given these congruences, if you are asked to prove triangles or other geometric shapes containing these points are congruent, you can use criteria such as SAS (Side-Angle-Side), ASA (Angle-Side-Angle), or others depending on the known elements. 5. If additional congruent parts (like another side or angle) are given or assumed, these can help establish congruence of entire triangles or figures. 6. Without extra information, such as the congruence of other sides or angles, we recognize that the given data establishes some congruent parts between the figures containing points C, E and U, W. Final answer: The given congruences state that the line segments $\overline{CE}$ and $\overline{UW}$ and the angles $\angle C$ and $\angle U$ are congruent, i.e., $|CE|=|UW|$ and $m\angle C = m\angle U$.