To prove a quadrilateral is a rhombus, establish that it is a parallelogram (opposite sides parallel) and demonstrate that opposite sides are congruent. Prove perpendicularity of diagonals, which also implies perpendicular bisectors of opposite sides. Additionally, demonstrate that diagonals bisect each other and angles, creating congruent triangles. These proofs collectively confirm that the quadrilateral satisfies all rhombus properties, proving its rhombus identity.
