The diagonals of the square ABCD intersect at the point O. The segment OF is the height of the triangle

The diagonals of the square ABCD intersect at the point O. The segment OF is the height of the triangle AOD. Are lines AB and OF parallel?

The diagonals of the square intersect at right angles, are halved and there are bisectors of the angles at the vertices.

Then the angle AAO = 45, the angle AOF = 45, since ОF is the height and bisector of the isosceles triangle of the AOD. Then the angle AOF = BAO = 45, and since these are cross-lying angles, AB is parallel to OF, which was required to prove.