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

Question

2820 views around the world

You can reuse this answer
Creative Commons License

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.

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