IN THE ADJOINING FIGURE,IF ANGLE 1=ANGLE 2,ANGLE 3 =ANGLE 4.ANGLE 2=ANGLE4, THEN FIND THE RELATION BETWEEN ANGLE1 AND ANGLE 3, USING EUCLIDS AXIOM.

Answer :

Given 

$\angle$ 1   =  $\angle$  2                                ------------------ ( 1 )

$\angle$ 3   = $\angle$ 4                                   ------------------ ( 2 )

$\angle$ 2   =  $\angle$ 4                                  ------------------ ( 3 )

And we know by first axiom of Euclid's " Things which are equal to the same thing are also equal to one another. " 

So , from equation 2 and 3 , we get 

$\angle$ 2  =  $\angle$ 3                 ----------- ( 4 )                 ( As both angles equal to same angle 4 , so we apply given axiom )

And

form equation 1 and 4 , we get 
As , we know " Things which are equal to the same thing are also equal to one another. " 

So,
$\angle$ 1    =  $\angle$ 3                                                                 (  Ans )