Show that the diagonals of a rhombus divide it into four congruent tri – InterviewSolution

1.	Show that the diagonals of a rhombus divide it into four congruent triangles.
Answer» Let the rhombus be ABCD and let there diameters intersect each other at O.Since,in a Rhombus all sides are equal,Therefore AB=ADand since ABCD isrhombus therefore its diagonals bisect each otherSo,AO=DOandAO=AO(common)ThereforeΔABO=~ΔADOSimilarly,ΔABO=~ΔBCOSimilarly,ΔBCO=~ΔDCOThereforeΔABO=~ΔBCO=~ΔCDO=~ΔADO

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