If two lines are cut by a transversal so that the corresponding angles are congruent, then these lines are parallel

n and m cut by transversal t

GIVEN: n and m cut by transversal t

 PROVE: n||m

 PROOF:

Suppose that n and m are not parallel. Then a line r can be drawn through point P that is
parallel to m; (r||m)

1:  - angles correspond r||m , transversal t

2:  - Given

3: -  From 2,3

4: - Definition of r

5: - From 3,4

Line r paraller to m

6: Then r and n must coincide, and it follows that n||m