Do Now A B C D 1.Name a line that does not intersect with line AC. 2.What is the intersection of lines AB and DB?

3.1 Identify Pairs of Lines and Angles 3.2 Use Parallel Lines and Transversals Objective: To identify angle pairs formed by three intersecting lines; to use angles formed by parallel lines and transversals

Parallel Lines Lines that do not Intersect and are coplanar

Parallel Planes Planes that Do not Intersect

Skew Lines Lines that do Not intersect and are not Coplanar.

Transversal Transversal: a line that intersects two or more coplanar lines.

Angles formed by a transversal There are 4 types of angles formed by a transversal.

Corresponding angles 1 5 Angles 1 and 5 are corresponding Because they have corresponding Positions.

Corresponding angles of Parallel Lines 1 5 The corresponding angles 1 and 5 Are congruent to each other Because lines k and m are parallel To each other. k m

Alternate Exterior Angles 1 Angles 1 and 8 are alternate Exterior angles because they are On alternate sides of the Transversal and are exterior Of the two lines. 8

Alternate Exterior angles of Parallel Lines 1 The alternate exterior angles 1 and 8 are congruent to each other because lines k and m are Parallel to each other. k m 8

Alternate Interior Angles Angles 3 and 6 are alternate interior angles because they are On alternate sides of the Transversal and on the interior Of the two lines. 3 6

Alternate Interior angles of Parallel Lines The alternate interior angles 3 and 6 are congruent to each other because lines k and m are Parallel to each other. k m 6 3

Consecutive Interior Angles Angles 4 and 6 are consecutive Interior angles because they are On the same side of the transversal And are inside the two lines. 4 6

Consecutive Interior angles of Parallel Lines The consecutive interior angles 4 and 6 are supplementary to each other because lines k and m are parallel to each other. k m 6 4

Parallel lines cut by a transversal. When two parallel lines are cut by a transversal the following relationships are true. –Corresponding angles are congruent –Alternate exterior angles are congruent –Alternate interior angles are congruent –Consecutive interior angles are supplementary.

Example 1: 1 5 Name all pairs of corrsponding, alternate interior, alternate exterior, and consecutive interior angles

Example: Classify the angle pair x y

m n

p q

Example 2: Solve for the variable 2p 120

Example 3: Solve for the variable x 80

Example 4: Find all the missing angle measures 105