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

Theorem - III:
If a transversal intersects a pair of parallel lines, then the interior angles on the same side of the transversal are supplementary.

Hypothesis:
l // m and a transversal 'p' intersects the two lines so that A and B are a pair of interior angles on the same side of the transversal and E and F is the other such pair.

Conclusion:
a. A + B = 180.
b. E + F = 180
Proof:
A and H form a linear pair,
Therefore, A + H = 180
But H = B (By the axiom of corresponding angles).
Therefore, Putting B in the place of H, we get
A + B = 180
Similarly we can also show that E + F = 180.,br>

Note:
According to the axiom-3 on corresponding angles, we know that if a transversal intersects two parallel lines, then the corresponding angles will be equal.


Directions: Draw parallel lines and a transversal and show that the interior angles on the same side of the transversal are supplementary.

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