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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 ĐA = ĐB. Conclusion: l // m. Proof: Let ĐC be the vertically opposite angle to ĐA. Then, ĐA = ĐC. but ĐA = ĐB given, Therefore, ĐB = ĐC. 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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