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
1 = 2 ------------------ ( 1 )
3 = 4 ------------------ ( 2 )
2 = 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
2 = 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,
1 = 3 ( Ans )
Given
1 = 2 ------------------ ( 1 )
3 = 4 ------------------ ( 2 )
2 = 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
2 = 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,
1 = 3 ( Ans )