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Middle/High School Algebra, Geometry, and Statistics (AGS)
5.6 Parallel Lines - Interior Angles are Supplementary - II

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. A and B are a pair of interior angles on the same side of the transversal such that,
A + B = 180.

l // m.

Let C be an angle forming a linear pair with A.
Then A + C = 180.
But A + B = 180, given.
Therefore, A + B = A + C.
Therefore, B = C
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.

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