Prove that the diagonals of a rhombus are perpendicular to each other.

Asked by Topperlearning User | 17th Aug, 2017, 07:45: AM

Expert Answer:


ABCD is a rhombus. AB = BC = DC
BO = OD; and AO = OC        (rhombus is a parallelogram, diagonals bisect each other)
In BOC and DOC
BO = DO,
BC = DC and OC = OC
BOCDOC                (SSS)
BOC = DOC              (c.p.c.t)
BOC + DOC = 180o       (linear pair)
Or BOC = DOC = 90o   
Hence, diagonals of a rhombus are perpendicular to each other.

Answered by  | 17th Aug, 2017, 09:45: AM