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Use the converse of the triangle proportionality theorem to identify parallel lines in the figure.
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Since ##(AM)/(MB)=16/8!=20/16=(AL)/(LC)## lines ##ML## and ##BC## are NOT parallel.
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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.
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Since ##(AM)/(MB)=16/8!=20/16=(AL)/(LC)## lines ##ML## and ##BC## are NOT parallel.
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Since ##(BK)/(KC)=15/12=20/16=(AL)/(LC)## lines ##LK## and ##AB## are parallel.
