Question

In parallelogram ABCD, point M is the midpoint of the side BC , point O is the intersection point of the segment AM and diagonal BD . Find the ratio BO:OD.

Answer 1

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,

$\triangle NOB\sim \triangle DOC$

Therefore,  $\frac{OB}{OD} = \frac{BN}{DC}$ = $\frac{BN}{2BN} = \frac{1}{2}$