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No.

If two lines intersect they cross each other.

To bisect each other, means that the lines not only intersect but that also that the point where the two line[ segment]s cross is the mid point of both of the line[ segment]s.

Examples, consider:

The diagonals of a kite ABCD with sides AB & AD equal (2 cm each), and BC & DC equal and twice the length of the other two sides (4 cm each). The diagonals AC and BD intersect each other; BD is bisected by AC but AC is NOT bisected by BD.

The diagonals of a right angle trapezium ABCD with ∠DAB and ∠ADC right angles (so sides AB and DC are parallel) and with sides AB = 2 cm, CD = 14 cm and AD = 5 cm (side BC = 13 cm). The diagonals AC and BD intersect, but NEITHER bisects the other.

The diagonals AC and BD of a square ABCD not only intersect each other, but they also do, in this case, bisect each other.

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Q: Does to intersect each other mean also to bisect each other?
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