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

Triangles ABE and EFC are similar, so \[\frac{ AD }{ EF }=\frac{ AE }{ EC }=\frac{ DE }{ FC }\] or
\[\frac{ 6 }{ EF }=\frac{ 12 }{ 18 }=\frac{ DE }{ 24 }\]

Solve for BD and DF
Then BD = EF and DE = BF because they're the sides of a parallelogram.