Question

The question for first is
In fig, it is given that AD = BC. By which Euclid's axiom it can be proved that AC = BD?

Second
In fig state which lines are parallel and why?

Answer 1

It is axiom 3.  If equals are subtracted from equals then the results are also equal.

AB = AB
AB - AD = AB - BC                subtracting equals  AD & BC

DB = AC
So                BD = AC

See diagram enclosed.  Your diagram is not clear. not properly visible
1,2,3 are straight lines.  4,5,6 are angles.

angle 6 = angle 5.
Since angle 5 = angle 4,  lines 1 and 2 are parallel. As they make same interior angle with straight line3.
Euclid's postulate 5 - parallel postulate.

Answer 2

Answer:

Step-by-step explanation:

It is axiom 3.  If equals are subtracted from equals then the results are also equal.

AB = AB

AB - AD = AB - BC                subtracting equals  AD & BC

DB = AC

So                BD = AC

See diagram enclosed.  Your diagram is not clear. not properly visible

1,2,3 are straight lines.  4,5,6 are angles.

angle 6 = angle 5.

Since angle 5 = angle 4,  lines 1 and 2 are parallel. As they make same interior angle with straight line3.

Euclid's postulate 5 - parallel postulate.