State the axioms of corresoning angle

Dear student,
It should be corresponding angles
We know " When two lines are crossed by another line (which is called the Transversal), the angles in matching corners are called corresponding angles. "



Here corresponding angles are  

( a , e )    and  ( b , f )  and  ( c , g ) and  ( d  , h ) 

And we know

 a   +    d     =   180°               ------ ( 1 )                  ( As we know sum of all angles on a line is equal to 180​°  )
And
d   +    e     =    180°             ------ ( 2 )                   ( Sum of two consecutive interior angles is equal to 180°  )
And
 e   +   h     =   180°               ------ ( 3 )                  ( As we know sum of all angles on a line is equal to 180​°  )

From equation 1 and 2 , we get

 a   +   d     =  ​ d   +   e    

 a     =   e    
And
from equation 2 and equation 3 , we get 

 d   +   e     =  ​ e   +   h  

 d     =   h  

Similarly we can proof
 b     =   f 
And
 c     =   g  

Hence , we can say that when two parallel line intersect by a transversal line ,than corresponding angles are equal to each other .                             ( Hence proved )
 

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