2. Place a patty paper over the set of angles <1, <2, <3, and <4 and copy the two intersecting lines onto the patty paper.

3. Slide the patty paper down and compare angles 1 through 4 with angles 5 through 8.

Warm-UpWarm-Up

1 23 4

3.2 Use Parallel Lines and 3.2 Use Parallel Lines and TransversalsTransversals

Objectives:

1.To find angle pair measurements with parallel lines cut by a transversal

2.To prove theorems involving parallel lines cut by a transversal

TransversalTransversal

A line is a transversaltransversal if and only if it intersects two or more coplanar lines.– When a transversal

cuts two coplanar lines, it creates 8 angles, pairs of which have special names

TransversalTransversal

• <1 and <5 are corresponding anglescorresponding angles

• <3 and <6 are alternate alternate interior anglesinterior angles

• <1 and <8 are alternate alternate exterior anglesexterior angles

• <3 and <5 are consecutive interior consecutive interior anglesangles

Four Window FoldableFour Window Foldable

Corresponding Angles Corresponding Angles PostulatePostulate

If two parallel lines are cut by a transversal, then pairs of corresponding angles are congruent.

Alternate Interior Angles Alternate Interior Angles TheoremTheorem

If two parallel lines are cut by a transversal, then pairs of alternate interior angles are congruent.

Four Window FoldableFour Window Foldable

Corresponding Angles Corresponding Angles PostulatePostulate

If two parallel lines are cut by a transversal, then pairs of corresponding angles are congruent.

Alternate Interior Angles Alternate Interior Angles TheoremTheorem

If two parallel lines are cut by a transversal, then pairs of alternate interior angles are congruent.

Parallel Line TheoremsParallel Line Theorems

Alternate Exterior Angle Alternate Exterior Angle TheoremTheorem

If two parallel lines are cut by a transversal, then pairs of alternate exterior angles are congruent.

Consecutive Interior Consecutive Interior Angles TheoremAngles Theorem

If two parallel lines are cut by a transversal, then pairs of consecutive interior angles are supplementary.

Example 1Example 1

On the map below, 1st and 2nd Ave. are parallel.

Example 1Example 1

A city planner proposes to locate a small park on the triangular island formed by the intersections of the four streets below.

Example 1Example 1

What are the measures of the three angles of the garden? Answer in your notebook

Example 2: SATExample 2: SAT

In the figure, if l || m, what is the value of x?

HINT: Find y 1st since there are

2 parts with y.

2y+25

x+15

3y

m

l

y=25x=10

Example 3: SATExample 3: SAT

In the figure, if l1 || l2 and l3 || l4, what is y in terms of x.

l4

l3

l2

l1

yy

x

y=180-x 2

THINK about it before you look at the answer and TRY!

Example 4Example 4

Prove the Alternate Interior Angle Theorem.

Given:

Prove:

l m

3 6

TRY IT!!!

Example 5Example 5

Given: and

Prove:

2 64m 7 64m

l m

You can EASILY do THIS one!

Example 7Example 7

Find the values of x and y if k || l || m.

l

k

m 2y+5

11x-1

7y-4

7x+9Did you try it??!?!

x=13.8y=11.2