In

ΔABC,DE‖BC,
where

D
is a point on AB and

E
is a point on AC, then

EC

DB

=
____.

Question

In

ΔABC,DE‖BC,
   where

D
   is a point on AB and

E
   is a point on AC, then

EC
    
     DB
   
   =
   ____.

Accepted Answer

In a

ΔABC,DE‖BC,
   where

D
   is a point on AB and

E
   is a point on AC, then

EC
    
     DB
   
   =

AE
    
     AD

.Consider the figure, We know,The Angle-Angle (AA) criterion for similarity of two triangles states that “If two angles of one triangle are respectively equal to two angles of another triangle, then the two triangles are similar”.According to the figure,

∠ABC=∠ADE         
      
       corresponding angles

∠ACB=∠AED         
      
       corresponding angles

The triangles

ΔADE
   and

ΔABC
   are similar by the AA axiom. So,

AB
    
     AD
   
   =
    
     AC
    
     AE

⇒
      
       AB
      
       AD
     
     =
      
       AC
      
       AE

⇒
      
       AD+DB
      
       AD
     
     =
      
       AE+EC
      
       AE

⇒1+
      
       DB
      
       AD
     
     =1+
      
       EC
      
       AE

⇒
      
       DB
      
       AD
     
     =
      
       EC
      
       AE

⇒
      
       AD
      
       DB
     
     =
      
       AE
      
       EC

⇒
      
       EC
      
       DB
     
     =
      
       AE
      
       AD

Therefore, the value of

EC
    
     DB
   
   =
    
     AE
    
     AD

.

In $Δ A B C, D E ‖ B C,$ where $D$ is a point on AB and $E$ is a point on AC, then $E C D B =$ ____.

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In ΔABC,DE‖BC, where D is a point on AB and E is a point on AC, then EC DB = ____.