Chapter 3: Parallel and Perpendicular Lines

Lesson 1: Parallel Lines and Transversals

Definitions Parallel lines ( || )- coplanar lines that do not

intersect (arrows on lines indicate which sets are parallel to each other)

Parallel planes- two or more planes that do not intersect

Skew lines- lines that do not intersect but are not parallel (are not coplanar)

Transversal- a line that intersects two or more lines in a plane at different points

Pairs of angles formed by parallel lines and a transversal

(see graphic organizer for examples)

Exterior angles: outside the two parallel lines Interior angles: between the two parallel lines Consecutive Interior angles: between the two

parallel lines, on the same side of the transversal Consecutive Exterior angles: outside the two

parallel lines, on the same side of the transversal Alternate Exterior angles: outside the two

parallel lines, on different sides of the transversal Alternate Interior angles: between the two

parallel lines, on different sides of the transversal Corresponding angles: one outside the parallel

lines, one inside the parallel lines and both on the same side of the transversal

ExamplesA. Name all segments parallel to BC.B. Name a segment skew to EH.C. Name a plane parallel to plane ABG.

Classify the relationship between each set of angles as alternate interior, alternate exterior, corresponding, or consecutive interior angles

A. 2 and 6 B. 1 and 7C. 3 and 8D. 3 and 5

Examples

Examples

A. Identify the sets of lines to which line a is a transversal.B. Identify the sets of lines to which line b is a transversal.C. Identify the sets of lines to which line c is a transversal.