Unit 6 Parallel Lines Learn about parallel line relationships Prove lines parallel Describe angle relationship in polygons

Lecture 1 Objectives State the definition of parallel lines Describe a transverse

Parallel Lines Coplanar lines that do not intersect. m n Skew lines are non-coplanar, non-intersecting lines. m || n p q *Coplaner means they are in the same plane

The Transversal Any line that intersects two or more coplanar lines. r s t

Special Angle Pairs Corresponding  1 and  5 Alternate Interior  4 and  5 Same Side Interior  4 and  6 r s t

Lecture 2 Objectives Learn the special angle relationships …when lines are parallel

When parallel lines are cut by a transversal… Corresponding  ’s   1   5 Alternate Interior  ’s   4   5 Same Side Interior  ’s Suppl.  4 suppl.  6 r s t

If two parallel lines are cut by a transversal, then corresponding angles are congruent. r s t

If two parallel lines are cut by a transversal, then alternate interior angles are congruent. r s t

If two parallel lines are cut by a transversal, then same side interior angles are supplementary. r s t

A line perpendicular to one of two parallel lines is perpendicular to the other. r s t

Lecture 3 Objectives Learn about ways to prove lines are parallel

If two lines are cut by a transversal so that corresponding angles are congruent, then the lines are parallel. 1 2 m n If  1   2, then m || n.

If two lines are cut by a transversal so that alternate interior angles are congruent, then the lines are parallel. 1 2 m n If  1   2, then m || n.

If two lines are cut by a transversal so that same side interior angles are supplementary, then the lines are parallel. 1 2 m n If  1 suppl  2, then m || n.

In a plane, two lines perpendicular to the same line are parallel. m n If t  m and t  n, then m || n. t

Two lines parallel to the same line are parallel to each other m n p If p  m and m  n, then p  n

Ways to Prove Lines are Parallel Corresponding angles are congruent Alternate interior angles are congruent Same side interior angles are supplementary In a plane, that two lines are perpendicular to the same line Both lines are parallel to a third line