Parallel and Perpendicular Lines, Summaries of Pre-Calculus

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Parallel and Perpendicular Lines Gl Parallel and Skew (p. 173) Parallel lines are coplanar lines that do not intersect. Skew lines are lines that do not intersect and are not coplanar. Parallel planes are planes that do not intersect. Angle Pairs Formed by Two Lines and a Transversal (p. 174) Interior angles lie in the region between lines that are intersected by a transversal. Exterior angles lie in the two regions that are not between lines that are intersected by a transversal. Consecutive interior angles are interior angles that lie on the same side of a transversal. Alternate interior angles are nonadjacent interior angles that lie on opposite sides of a transversal. Alternate exterior angles are nonadjacent exterior angles that lie on opposite sides of a transversal. Corresponding angles lie on the same side of a transversal and on the same side of two lines that are intersected by the transversal. Postulate 3.1 Corresponding Angles (p. 180) If two parallel lines are cut by a transversal, then each pair of corresponding angles is congruent. Theorem 3.1 Alternate Interior Angles Theorem (p. 181) If two parallel lines are cut by a transversal, then each pair of alternate interior angles is congruent.