Geometry (please help, quick)

Question

Theorem: A line parallel to one side of a triangle divides the other two proportionately.

In the figure below, segment DE is parallel to segment BC and segment EF is parallel to AB:

Which statement can be proved true using the given theorem?

Segment BD = 12

Segment BD = 4

Segment BF = 16

Segment BF = 9

Answer 1

By the Side Splitter Theorem, 6 / BD = 12 / 18. So, BD = 9.

Similarly, 24 / BF = 18 / 12. So, BF = 16.