|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.
'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°.
l // m.
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 axiom-4, '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.