Parallelograms diagonals bisect

Parallelogram's diagonals bisect each other

Consider parallelogram ABCD whose diagonals AC, BD intersect at E.

∠DAC = ∠ACB ...(Alt. ang.s on parallels DA BC)

∠ADB = ∠CBD ...(Alt. ang.s on parallels DA BC)

AD = BC ...(Opp. sides of parallelogram are equal)

∴ ∇ADE ≡ ∇CEB ...Two angles and incl. side equal)

∴ DE = EB and AE = EC