Bell Work• Classify the following angle relationships• A) 1 and 5 B) 1 and 8• C) 4 and 6 D) 3 and 6• E) 5 and 6 F) 2 and 4• Find the value of the variables if the lines are ||• A) x = B) x =• y = y =

Outcomes

• I will be able to:• 1) Use properties of parallel lines to determine

congruent or supplementary angles

• 2) Prove lines are parallel

• 3) Find values of angles that prove lines are parallel

Proving lines are Parallel

• *** All of the converses from Section 3.3 are true as well. For example, if we can show that corresponding angles are congruent, then the two lines cut by the transversal must be parallel.

Proving Lines are Parallel

the lines are parallel

Because corresponding anglesare congruent, we know line a ІІ line b.

Proving Lines are Parallel

• Because Alternate Interior Angles are congruent,

we know line a ІІ line b.

the lines are parallel

Proving Lines are Parallel

• Because Same Side Interior Angles are supplementary, we know that line a ІІ line b.

the lines are parallel

Proving Lines are Parallel

• Because Alternate Exterior Angles are congruent,

we know line a ІІ line b.

the lines are parallel

Using Theorems To Prove Lines are Parallel

Given

TransitiveProperty ofCongruence

AD ІІ BC Alternate InteriorAngles are congruent

Using Theorems to Prove Lines are Parallel

• What relationship do we have with angles?• They must be congruent if the two lines are

parallel

5312 xx

x = 6

Using Theorems to Prove Lines are Parallel

• 3. You notice that when your windshield wipers on your car stopped they each made a 30° angle with the bottom of the windshield. If the wipers were long enough, would they ever cross each other? Explain your answer.

• Picture:

30° 30°

Using Theorems to Prove Lines are Parallel

What types of angles arethe two angles we are comparing?

Line m ІІ Line n by the Alternate Exterior Angles Converse

Using Theorems to Prove Lines are Parallel

What angles are wegoing to compare?

Line a ІІ Line b by the Alternate InteriorAngle Converse.

Exit Quiz

• Are the lines a and b parallel? Why or why not?

• a) b)

• c) d)