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Geometry: Section 3.3 Properties of Parallel Lines Two lines are parallel iff they are coplanar and do not intersect. To indicate that AB is parallel to CD AB // CD 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 two lines that intersect to form right angles. 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 there is exactly one line through the point that will be perpendicular to the given line 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. 3 x 5 7 x 11 16 4 x 4x Examples: Find the value of the variable in each problem. 3 y 5 7 y 11 180 10 y 6 180 10 y 186 y 18.6 Examples: Find the value of the variable in each problem. 5w 8 3w 6 180 8w 14 180 8w 166 w 20.75 Theorem 3.7 Perpendicular Transversal Theorem If a transversal is perpendicular to one of two parallel lines, then the transversal is also perpendicular to the second parallel line.