Geometry: Section 3.3 Properties of Parallel Lines

Two lines are parallel iff they are coplanar and do not intersect. To indicate that is parallel to we write _______ Arrowheads are use to indicate parallel lines in a figure.

Noncoplanar lines which do not intersect are called skew.

Recall that perpendicular lines are

Postulate 13: The Parallel Postulate If there is a line and a point not on the line, then there is exactly one line through the point that will be parallel to the given line.

Postulate 14: The Perpendicular Postulate If there is a line and a point not on the line, then

Postulate 15 Corresponding Angles Postulate (CAP) If two parallel lines are cut by a transversal, then corresponding angles are congruent.

Theorem 3.4 Alternate Interior Angles Theorem (AIAT) If two parallel lines are cut by a transversal, then alternate interior angles are congruent.

Theorem 3.5 Same-Side Interior Angles Theorem (SSIAT) If two parallel lines are cut by a transversal, then same-side interior angles are supplementary.

Theorem 3.6 Alternate Exterior Angles Theorem (AEAT) If two parallel lines are cut by a transversal, then alternate exterior angles are congruent.

Examples: Find the value of the variable in each problem.

Theorem 3.7 Perpendicular Transversal Theorem If a transversal is perpendicular to one of two parallel lines, then