GEOMETRY 3.1. Parallel Lines and Transversals Do Now: Homework? Questions? Comments? Confusions? Concerns? ASK ASK ASK ASK! Definitions: Parallel Lines: are coplanar lines that do not intersect. Notation: Picture: Arrows are used to indicate that lines are parallel. Definitions Skew Lines: Are lines that do not intersect and are not coplanar. What other skew lines are in this picture? Definitions (Continued) Parallel Planes: are planes that do not intersect. Notation: None Example 1: Identify each of the following using the wedge of cheese below. a) All segments parallel to JP b) A segment skew to KL c) A plane parallel to plane PQR Example 2: In the figure, assume that the lines and planes that appear to be parallel are parallel. Which segments are parallel to AB? Which segments are skew to CD? What are two pairs of parallel planes? What are two segments parallel to plane BCGF? You Try! Definition: Transversal: A line that intersects two or more coplanar lines at two different points. Notation: None Picture: t is a transversal of lines l and m Definitions: Interior Angles: Angles that lie in the region between two lines. Here interior angles are: Definitions: Exterior Angles: Angles that lie in the region outside of two lines. Here exterior angles are: Definitions: Consecutive Interior Angles: Interior Angles that lie on the same side of a transversal. Here consecutive interior angles are: Definitions: Alternate Interior Angles: are nonadjacent interior angles that lie on opposite sides of a transversal. Alternate Interior Angles: Definitions: Alternate Exterior Angles: are nonadjacent exterior angles that lie on opposite sides of a transversal. Alternate Exterior Angles: Definitions: Corresponding Angles: lie on the same side of a transversal and on the same side of the two lines the transversal intersects. Corresponding angles: Example 3: Alternate Interior Angles? Alternate Exterior Angles? Corresponding Angles? Consecutive Interior Angles? You Try! Alternate Interior Angles? Alternate Exterior Angles? Corresponding Angles? Consecutive Interior Angles? Example 4: Determine the relationship between each set of angles 1.< 2 and