Final answer:
The question deals with proving the congruence of different pairs of triangles given certain geometric conditions. Triangle congruence criteria such as SSS, SAS, ASA, and AAS would likely be used in these proofs, highlighting the importance of geometry in solving such problems.
Step-by-step explanation:
It appears that the question concerns various geometric proofs relating to triangles and their properties in congruency and similarity. Understanding these questions typically involves applying theorems and postulates for congruent triangles such as SSS (Side-Side-Side), SAS (Side-Angle-Side), ASA (Angle-Side-Angle), and AAS (Angle-Angle-Side). The student seems to be given certain conditions, such as AD = AB and CA bisecting ∠BAD, and is tasked with proving the congruence of four pairs of triangles under these conditions.
The proofs would likely involve showing that the triangles have equal side lengths and angles in corresponding positions, demonstrating congruence through one of the congruence criteria. We do not have the specific figure to reference, so providing accurate proofs for these particular triangles is not possible. However, it is clear that geometric proofs and triangle congruence are the focal points of this exercise.