Question

In $\triangle ABC$, D and E are points on sides AB and AC respectively such that AD ✕ EC = AE ✕ DB. Prove that $DE \parallel BC$.

Answer 1

Answer:

It is proved that DE || BC .

Step-by-step explanation:

Given :  

In ∆ABC, D and E are points on sides AB and AC and AD ✕ EC = AE ✕ DB.  

Since, AD ✕ EC = AE ✕ DB

AD/DB = AE/EC  

By Converse of basic proportionality theorem

DE || BC  

Hence, it is proved that DE || BC .

CONVERSE OF BASIC PROPORTIONALITY 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.

HOPE THIS ANSWER WILL HELP YOU ..

Answer 2

Heya!

Here is ur answer....

_____________________________

Given :

In ΔABC,

D and E are the points on sides AB and AC respectively..

Such that,

AE ×EC = AE × DB

RTP:

DE || BC

PROOF :

In ΔABC,

AD×EC = AE×DB

AD/DB = AE/EC

Since, AB/DB = AE/EC

Therefore,

DE||BC

[From Converse of BPT theorem]

Hence proved!

Hope it helps u..