Question

BPT theorem class 10 in triangle​

Answer 1

Basic Proportionality Theorem (B.P.T)

Statement: If a line is drawn parallel to one side of a triangle to intersect the other two sides in distinct points, then the other two sides are divided in the same ratio.

Given: In  △ABC , line  DE  is drawn parallel to side  BC  which meets  AB  at  D  and  AC  at  E  .

To Prove:  

AD /DB = AE /EC

 

 

Proof:

 Statements Reasons

In  △ABC  and  △ADE ,    

  ∠ABC   =  ∠ADE  Corresponding angles

  ∠ACB   =   ∠AED  Corresponding angles

  ∠BAC   =  ∠DAE  Common (shared angle)

∴   △ABC∼△ADE  By  AA∼  

   

AB /AD = AC /AE

 

  Corresponding sides of similar tringles are proportional

⇒    

AD+DB  = AE+EC

____       _____

AD               AE

 

⇒    1+ DB /AD =1+ EC /AE

 

AD /AD =1  ;   AE /AE =1  

⇒     DB /AD = EC /AE

 

  Cancelling 1 from both the sides

⇒     AD /DB = AE /EC

 

  Taking the reciprocal