Question

prove converse of BPT​

Answer 1

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 2

Answer:

Refer the attachment... hope it helps...