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Proof :
If a line is drawn parallel to one side of a triangle intersecting other two sides, then it divides the two sides in the same ratio.
Example :
1) In the given figure, PQ || MN.
If KP / PM = 4 /13 and KN = 20.4 cm.
Find KQ.
Solution :
In Δ KMN,
PQ || MN
∴ KP / PM = KQ / QN ( By BPT theorem)
⇒ KP / PM = KQ / ( KN – KQ)
⇒ 4 / 13 = KQ / ( 20.4 – KQ)
⇒ 4( 20.4 - KQ ) = 13 KQ ( cross multiply )
⇒ 81.6 – 4KQ = 13 KQ
⇒ 17KQ = 81.6
⇒ KQ = 81.6 / 17.
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