Theorem  V:
If a transversal intersects two coplanar lines in such a way that a pair of interior angles on the same side of the transversal are supplementary, then the two lines are parallel.
Hypothesis:
'l' and 'm' are two coplanar lines. 'p' is the transversal intersecting them. ÐA and ÐB are a pair of interior angles on the same side of the transversal such that,
ÐA + ÐB = 180°.
Conclusion:
l // m.
Proof:
Let ÐC be an angle forming a linear pair with ÐA.
Then ÐA + ÐC = 180°.
But ÐA + B = 180°, given.
Therefore, ÐA + ÐB = ÐA + ÐC.
Therefore, ÐB = ÐC
That is the corresponding angles are equal.
So by axiom4, 'l' and 'm' must be parallel lines.
Therefore, l // m.
Directions: Draw parallel lines and a transversal and show that the interior angles are supplementary.
