Final answer:
By proving triangle congruence (ΔABD is congruent to ΔCDB), diagonals of a parallelogram are shown to bisect one another, thus supporting the notion that each diagonal splits the parallelogram into two congruent triangles.
Step-by-step explanation:
If you prove that ΔABD is congruent to ΔCDB, you have effectively demonstrated that the diagonals of a parallelogram bisect each other. This conclusion is based on the congruence of triangles which implies that corresponding parts of the congruent triangles are equal, which includes the halves of the parallelogram's diagonals where the triangles intersect. Hence, proving the congruence of ΔABD and ΔCDB validates the statement that diagonals of a parallelogram bisect each other. In other words, each diagonal divides the parallelogram into two congruent triangles. To further understand the concept, we can see that the parallelogram rule used in vector addition and subtraction also reflects the properties of a parallelogram in geometry. When vectors are represented with sides of a parallelogram, the resultant or difference vector is represented by a diagonal, which does not simply comprise the lengths of the sides but instead is determined using the laws of trigonometry and the Pythagorean theorem, indicating the complex nature of geometric constructions.