Final answer:
Without additional specific information on the sides and angles of triangles ADC and EBC, it is impossible to conclude their congruence. We need measurable elements matching one of the congruence rules like SSS, ASA, or SAS to confirm congruence.
Step-by-step explanation:
The student has asked whether triangles ADC and EBC are congruent. To determine the congruence of the two triangles, we need to compare their corresponding sides and angles. In geometry, triangles are congruent if they satisfy certain conditions such as Side-Side-Side (SSS), Angle-Side-Angle (ASA), or Side-Angle-Side (SAS). The description of triangles ADC and EBC sharing angle ACE, point B on segment AC, point D on segment EC, segments AD and EB intersecting at point F, and segments BC and DC each marked with one dash indicates that these triangles are potentially congruent by either SSS, ASA, or SAS.
However, based on the given description alone, we do not have enough information to definitively conclude that triangles ADC and EBC are congruent. We would require more specific information regarding the sides and angles of the triangles to apply one of the congruence rules. For instance, we would need to know if two sides and the included angle of one triangle are equal to two sides and the included angle of the other triangle to determine congruence by SAS, but this information is not provided.