In a parallelogram abcd point k belongs to diagonal bd so that bk: dk=1: 4. if the extension of ak meets bc at point e, what is the ratio of be: ec?

Step-by-step explanation:

In the diagram below we have

ABCD is a parallelogram. K is the point on diagonal BD, such that

And AK meets BC at E

now in Δ AKD and Δ BKE

∠AKD =∠BKE                ( vertically opposite angles are equal)

since BC ║ AD and BD is transversal

∠ADK = ∠KBE     ( alternate interior angles are equal )

By angle angle (AA) similarity theorem

Δ ADK  and Δ EBK are similar

so we have

    ( ABCD is parallelogram so AD=BC)

        ( BC= BE+EC)

 ( subtracting 1 from both side )

taking reciprocal both side