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 angles are 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 Transitive Property of Congruence AD ІІ BC Alternate Interior Angles are congruent

Using Theorems to Prove Lines are Parallel Which angle relationships do we have? They must be congruent if the two lines are parallel 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 are the 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 we going to compare? Line a ІІ Line b by the Alternate Interior Angle Converse.

Exit Quiz Are the lines a and b parallel? Why or why not? a) b) c) d)

Exit Quiz Key A) Yes, lines a and b are parallel because alternate interior angles are congruent. B) Yes, lines a and b are parallel because corresponding angles are congruent. C) No, lines are not parallel because alternate exterior angles are NOT congruent. D) No, Same Side Interior angles are not supplementary, so the lines are NOT parallel.