# 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

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

From equation 1 and 2 , we get

$\angle$ a   +  $\angle$ d     =  ​$\angle$ d   +  $\angle$ e

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

$\angle$ d   +  $\angle$ e     =  ​$\angle$ e   +  $\angle$ h

$\angle$ d     =  $\angle$ h

Similarly we can proof
$\angle$ b     =  $\angle$ f
And
$\angle$ c     =  $\angle$ 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 )

• 1
What are you looking for?