Prove the diagonals of a parallelogram bisect each other, i.e. #bar(AE) = bar(EC)# and #bar(BE) = bar(ED)# ?

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Answer 1 · 2016-09-12T18:41:01

See Proof in Explanation.

#ABCD# is a parallelogram

#:. AB || DC, and, AB=DE................(1)#

#:. m/_ABE=m/_EDC, m/_BAE=m/_ECD..........(2)#.

Now, consider #DeltaABE and DeltaCDE. Because of #(1) and (2)#,

#DeltaABE~=DeltaCDE#.

#:. AE=EC, and, BE=ED#

Hence, the Proof.