In ΔABC M and X are the midpoints of the sides AB and BC, respectively.
∴ MX || AC (Mid-point theorem)
Similarly, YN || AC
∴ MN || YN
Remember: Two lines which are parallel to a line are parallel to each other.
Similarly, NX || MY
Hence, statement 1 is incorrect.
In quadrilateral MXNY, NX || MY and MX || YN
∴ MXNY is a parallelogram
⇒ is the mid-point of MN and XY.
Remember: Diagonals of a parallelogram bisect each other.
ABCD is a parallelogram.
⇒O is the mid-point of AC and BD
So, the straight lines AC, BD, XY andMN meet at a point.
Hence, statement 2 is correct