Show that each diagonal of a rhombus bisects the angle through which it passes.

(i) In ΔBOC and ΔDOC

BO = DO [In a rhombus diagonals bisect each other]

CO = CO Common

BC = CD [All sides of a rhombus are equal]

ΔBOC≅ΔDOC [SSS Congurency]

∠BCO =∠DCO from above [corresponding parts of congruent triangles]

Hence, each diagonal of a rhombus bisect the angle through which it passes.