Lines Angles and Triangles


   
 
Converse of Theorem 3
Statement
 
If a transversal intersects two lines in such a way that a pair of consecutive interior angles are supplementary, then the two lines are parallel.
 
 
Given:
 

 
To prove:
 
AB||CD
 
Proof:
 
…(i) [Linear pair (ray FB stands on EFGH)]
 
 
( Corresponding angles postulate)
 
 
…(ii) ( given)
 
From (i) and (ii), we have
 
 
 
These are corresponding angles.
 
AB || CD
 
  
     
   
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