Prove that the diagonals of a parallelogram bisect each other.

Asked by Topperlearning User | 16th Aug, 2017, 02:15: PM

Expert Answer:

 
ABCD is a parallelogram, diagonals AC and BD intersect at O
In triangles AOD and COB,
DAO = BCO                               (alternate interior angles)
AD = CB
ADO = CBO                               (alternate interior angles)
AOD COB                           (ASA)
Hence, AO = CO and OD = OB          (c.p.c.t)
Thus, the diagonals of a parallelogram bisect each other.

Answered by  | 16th Aug, 2017, 04:15: PM