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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.
This is one of them (AAS). For a list see Congruent Triangles. If there are two pairs of corresponding angles and a pair of corresponding opposite sides that are equal in measure, then the triangles are congruent. By opposite side we mean a side opposite either one of the angles.