Parallel Lines and Planes What You'll Learn You will learn to describe relationships among lines, parts of lines, and planes. In geometry, two lines in a plane that are always the same distance apart are ____________. parallel lines No two parallel lines intersect, no matter how far you extend them.

Parallel Lines and Planes Definition of Parallel Lines Two lines are parallel iff they are in the same plane and do not ________. intersect

Parallel Lines and Transversals What You'll Learn You will learn to identify the relationships among pairs of interior and exterior angles formed by two parallel lines and a transversal.

Parallel Lines and Transversals In geometry, a line, line segment, or ray that intersects two or more lines at different points is called a __________ transversal B A l m 1 2 4 3 5 6 8 7 is an example of a transversal. It intersects lines l and m. Note all of the different angles formed at the points of intersection.

Parallel Lines and Transversals Definition of Transversal In a plane, a line is a transversal iff it intersects two or more Lines, each at a different point. The lines cut by a transversal may or may not be parallel. l m 1 2 3 4 5 7 6 8 Parallel Lines t is a transversal for l and m. t 1 2 3 4 5 7 6 8 b c Nonparallel Lines r is a transversal for b and c. r

Parallel Lines and Transversals Two lines divide the plane into three regions. The region between the lines is referred to as the interior. The two regions not between the lines is referred to as the exterior. Exterior Interior

Parallel Lines and Transversals When a transversal intersects two lines, _____ angles are formed. eight These angles are given special names. l m 1 2 3 4 5 7 6 8 t Interior angles lie between the two lines. Exterior angles lie outside the two lines. Alternate Interior angles are on the opposite sides of the transversal. Alternate Exterior angles are on the opposite sides of the transversal. Consectutive Interior angles are on the same side of the transversal. ?

Transversals and Corresponding Angles What You'll Learn You will learn to identify the relationships among pairs of corresponding angles formed by two parallel lines and a transversal.

Transversals and Corresponding Angles When a transversal crosses two lines, the intersection creates a number of angles that are related to each other. Note 1 and 5 below. Although one is an exterior angle and the other is an interior angle, both lie on the same side of the transversal. Angle 1 and 5 are called __________________. corresponding angles l m 1 2 3 4 5 7 6 8 t Give three other pairs of corresponding angles that are formed: 4 and 8 3 and 7 2 and 6