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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.

Hypothesis:
'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.

Conclusion:
l // m.

Proof:
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.