Question #e6e98

1 Answer
sankarankalyanam
Feb 8, 2018

As explained

Explanation:

enter image source here

Given #bar(KL) |\| bar(MN)#

In triangles JKL, KMN

#JhatKL = JhatMN, JhatLK = JhatMN# as KL parallel MN and corresponding angles. #hatJ# common.

Therefore TrianglesJKL & JMN are similar and hence the corresponding sides of the two trianglesa will be in the same proportion.

i.e. #(JK) / (JM) = (JL) / (JN) = (KL) / (MN)#

Can also be written as

#(JK) / (JK + KM) = (JL) / (JL + LN) = (KL) / (MN)# or

#(JM - KM) / (JM) = (JN - LN)) / (JN) = (KL) / (MN)#

enter image source here

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