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:

the figure shows triangle abc with segments de and ef. point d is on side ab, point e is on side ac, and point f is on side bc. segment ad is 6, segment ae is 12, segment ec is 18, and segment fc is 24.

which statement can be proved true using the given theorem?

segment bd = 12
segment bd = 4
segment bf = 16
segment bf = 9

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)

Segment BF = 16 is true.

Step-by-step explanation:

step-by-step explanation:

to find if any function is an inverse of the other, put the first equation in as x in the next one. then simplify and solve. if at the end you get the statement y = x, then it is an inverse. if you get anything else, it is not.