So, in the figure below, if k || l, then 2 8 and 3 5.
Since k || l, by the Corresponding Angles Postulate,
Therefore, by the definition of congruent angles,
m1 = m5.
m1 + m2 = 180°.
Also, 5 and 8 are supplementary, so
m5 + m8 = 180°.
Substituting m1 for m5, we get
m1 + m8 = 180°.
Subtracting m1 from both sides, we have
m8 = 180° − m1 = m2.
Therefore, 2 8.
You can prove that 3 5 using the same method.
The converse of this theorem is also true; that is, if two lines k and l are cut by a transversal so that the alternate interior angles are congruent, then k || l.