In a parallelogram, opposite sides are equal in length and opposite angles are equal in measure. Given the parallelogram LONM, we want to find the length of OM.
In any parallelogram, diagonals bisect each other. This means that if you draw the diagonals of LONM, point O, where the diagonals intersect, will be the midpoint of both diagonal LN and diagonal OM.
Therefore, since OM is one of the diagonals of the parallelogram, and knowing that both segments of the diagonal are equal, we can say that OM equals the length of ON.
If you have specific lengths for LO and LN (the sides of the parallelogram), you can apply the properties of parallelograms to confirm the exact lengths of all segments involved. If you know any other measurements or specifics about angles, you can make further calculations based on that information to establish the exact value of OM.