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
BOC
DOC (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.
AB = BC = DCBOC and DOCBOCDOC (SSS)BOC = DOC (c.p.c.t)BOC + DOC = 180o (linear pair)BOC = DOC = 90o Answered by | 17th Aug, 2017, 09:45: AM
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