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Two segments A C and B D bisect each oth...

Two segments `A C` and `B D` bisect each other at `O` . Prove that `A B C D` is a parallelogram.

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To prove: ABCD is a parallelogram
construction:AB,BC,CD and DA are joined
proof: in triangles AOB and COD
OA=OC (given)
OB=OD (given)
`/_AOB=/_COD` (Vertically opposite angles)
therefore, triangles `AOB=~COD` (SAS) `=> /_OAB=/_COD `(CPCT)
`=> ABIICD` → [1]
also AB=CD → [2]
from[1] & [2],
ABCD is a parallelogram
hence proved
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