angle 1=angle 4 and angle 3 =angle 2 by which euclid's axiom , it can be shown that if - Maths - Introduction to Euclid\s Geometry

Question

angle 1=angle 4 and angle 3 =angle 2 by which euclid's axiom ,
it can be shown that if angle 2= angle 4 then angle1= angle 3

Kshitij Sunil · Accepted Answer

It can be shown by Euclid's first axiom which states that:
"Things which are equal to the same things are equal to one
another "
Here, angle 1 = angle 4 (1)
angle 3 = angle 2 (2)
If, angle 2 = angle 4
then, angle 3 = angle 1 [Substituting values of angle 2 and
angle 1 from (1) and (2)]
or, angle 1 = angle 3

angle 1=angle 4 and angle 3 =angle 2. by which euclid's axiom , it can be shown that if angle 2= angle 4 then angle1= angle 3.