Final answer:
Triangle ABC and triangle DCB in square ABDC with diagonal CB are congruent because the diagonals of a square are equal, bisect each other at right angles, and bisect the vertex angles, forming two congruent right triangles.
Step-by-step explanation:
The question pertains to the properties of diagonals in a square, specifically in reference to square ABDC with diagonal CB. In a square, the diagonals are equal in length, bisect each other at right angles, and bisect the angles at the vertices they connect. Therefore, triangle ABC and triangle DCB are congruent by the SAS postulate (Side-Angle-Side), since they share the side CB (the diagonal), have equal sides AB and DC (since they are both sides of the square), and have right angles at vertex B since the diagonal bisects the angles of a square. These properties result in two congruent right triangles with a common hypotenuse CB and equal legs AB and DC.