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The diagonals of a parallelogram bisect ...

The diagonals of a parallelogram bisect each other.

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`ABCD` is a parallelogram, diagonals `AC` and `BD` intersect at `O`
In `triangleAOD` and `triangleCOB`,
`angleDAO=angleBCO` (alternate interior angles)
`AD=CB`
`angleADO=angleCBO` (alternate interior angles)
`triangleAOD~=triangleCOB` (By `ASA`)
Hence, `AO=CO` and `OD=OB` (By `CPCT`)
Thus, the diagonals of a parallelogram bisect each other.
Hence proved.
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