Rhombus Diagonal Bisector Property: Geometric Analysis and Verification

To solve the problem, let's review a fundamental property of rhombuses:

• In a rhombus, the diagonals have a special property: they intersect each other at right angles (90 degrees) and bisect each other. This means each diagonal cuts the other into two equal halves.

Why is this the case? Consider the fact that a rhombus is a type of parallelogram with all sides of equal length. Therefore, each diagonal acts as a line of symmetry, dividing the rhombus into two congruent triangles. This symmetry ensures that the diagonals not only intersect at right angles but also bisect each other.

In summary, given that the shape in question is a rhombus, we can confidently state that the diagonals do bisect each other.

Therefore, the answer to the problem is Yes.