MAHARASHTRA Class 10: Basic Proportionality Theorem and Angle Bisector Theorem Videos | Converse of BP theorem

If a line divides any two sides of a triangle in the same ratio, then the line must be parallel to the third side.

KP = 1.4 cm, KM = 5.6 cm PM = KM − KP = 5.6 − 1.4 = 4.2 cm KQ = 1.8

QN = KN − KQ = 7.2 - 1.8 = 5.4

Now, 

KP/PM = KQ/QN = 1/3

PQ is parallel to MN by the converse of BPT. 

Explanation:

In ∆ABC, AD/DB = 3/5

AE/EC = 4/8 = ½

AD/DB ≠ AE/EC DE is not parallel to BC.