Answer: BO:OD = 1:2
Step-by-step explanation:
Here, ABCD is parallelogram, point M is the midpoint of the side BC , point O is the intersection point of the segment AM and diagonal BD.
Let N is the mid point AB ⇒ AN=NB or 2.BN=DC. ( because AB=DC)
And join Points N and C. (by construction)
Then, In triangles NOB and DOC,
∠NOB=∠DOC ( vertically opposite angles)
And, ∠OBN = ∠ODC ( By the property of interior alternative angles by same transversal)
Thus, By the property of similarity,

Therefore,
= 