prove converse of BPT
Answers
Step-by-step explanation:
REF. image
converse of basic propotinality theorm statement :If a line divide any two sides of a triangle in the same ration , then the line must be parallel (ll) to the third side .
If AD /DE = AE/EC then DE ll BC
Prove that : DE ll BC
Given in triangle ABC , D and E are two points of AB and AC respectively , such that ,
AD / DB = AE/EC (1)
Let us assume that in triangle ABC , the point F is intersect on the side AC . So we can apply the :
Thales theorm ,
AD / DB = AF / FC (2)
Simplify (1st and 2nd ):
AE/ EC = AF / FC
adding 1 on both sides
AE/ EC +1 = AF/FC+1
------->AE+EC /Ec = AF+FC/ FC
-------> AC /EC = AF / FC
---------> AC = FC
From the above points we can see that the points E and F are coincide on AC , i.e., DF coincide with DE . Since DF is parallel to BC , DE is also parellel to BC
therefore , hence the converse of basic propotionally theorm is proved ........
hope it helps you a lot.......
Answer:
Refer the attachment... hope it helps...

