Use the converse of the triangle proportionality theorem to identify parallel lines in the figure.

Since
##(AM)/(MB)=16/8!=20/16=(AL)/(LC)##
lines ##ML## and ##BC## are NOT parallel.

Since
##(BK)/(KC)=15/12=20/16=(AL)/(LC)##
lines ##LK## and ##AB## are parallel.

Let’s first formulate triangle proportionality theorem and a converse to it.

Triangle proportionality theorem states that if ##DE## ##||## ##BC## then
##(AD)/(DB)=(AE)/(EC)##
Converse theorem states that if ##(AD)/(DB)=(AE)/(EC)## then ##DE## ##||## ##BC##
Applied to the picture above and assuming that the top right vertex of a triangle is ##B##, below it -point ##K## and segments ##BK## and ##KC## have corresponding lengths ##15## and ##12##, we can check the condition of parallelism as follows.

Since
##(AM)/(MB)=16/8!=20/16=(AL)/(LC)##
lines ##ML## and ##BC## are NOT parallel.

Since
##(BK)/(KC)=15/12=20/16=(AL)/(LC)##
lines ##LK## and ##AB## are parallel.