Prove that if a parallelogram is a rhombus then each diagonal bisects a pair of opposite angles. complete the proof. since jklm is a rhombus jm~= lm and jk~=lk. mk~=mk by the reflective property of congruence. so, mjk~=mlk by the (asa, sas, sss) triangle congruence theorem. therefore, jmk~= (mln, mnl, lmk) and jkm~=(lkn, lkm, lnk) by cpctc so mk bisects jml and jkl. is similar argument shows that jl bisects mjk and mlk