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A linear pair is formed when two adjacent angles have their non-common side in opposite rays. Their measures will always add up to 180 degrees. Vertival angles are formed by two intersecting lines. Two pairs are formed; they are across from each other (not adjacent), and are congruent.
Two lines are parallel if and only if the two angles of any pair of corresponding angles of any transversal are congruent (equal in measure). Note: This follows directly from Euclid's parallel postulate. Further, if the angles of one pair are congruent, then the angles of each of the other pairs are also congruent. In our images with parallel lines, corresponding angle pairs are: Î±=Î±1, Î²=Î²1, Î³=Î³1 and Î´=Î´1.