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 bf = 16
segment bd = 20
segment bd = 15
segment bf = 32

Segment BF = 16 is true.

Step-by-step explanation:

Since, DE is parallel to BC, so DE will divide AB and AC proportionally.

Hence,

⇒   

{Since, given that AE = 12, EC = 18 and AD = 6}

⇒ BD = 9.

Again, since, EF is parallel to AB, so EF will divide BC and AC proportionally.

Hence,

⇒   

{Since, given that AE = 12, EC = 18 and FC= 24}

⇒ BF = 16.

Therefore, segment BF = 16 is true. (Answer)

$12. that is my answer.