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Middle/High School Algebra, Geometry, and Statistics (AGS)
5.7 Parallel Lines - Corresponding Angles

Axiom - 4:
If a transversal intersects two coplanar lines, so that a pair of corresponding angles are equal, then the two lines are parallel.

Theorem - IV:
If a transversal intersects two coplanar lines in such a way that pair of Alternate angles are equal, then the two lines are parallel.

Hypothesis:
'l' and 'm' are two coplanar lines. 'p' is the transversal intersecting them so that a pair of alternate angles A = B.

Conclusion:
l // m.

Proof:
Let C be the vertically opposite angle to A.
Then, A = C.
but A = B given,
Therefore, B = C.
That is the corresponding angles are equal.
Therefore, by axiom-4 'l' must be parallel to 'm'.
Hence l // m.


Directions: Draw a pair of parallel lines and a transversal and show that the corresponding angles are equal.

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