1. 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 =

2. 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

3. 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.

4. Proving Lines are Parallel
the lines are parallel
Because corresponding angles
are congruent,
we know line a ІІ line b.

5. Proving Lines are Parallel
Because Alternate Interior Angles are congruent,
we know line a ІІ line b.
the lines are parallel

6. Proving Lines are Parallel
Because Same Side Interior Angles are supplementary, we know that line a ІІ line b.
the lines are parallel

7. Proving Lines are Parallel
Because Alternate Exterior Angles are congruent,
we know line a ІІ line b.
the lines are parallel

8. Using Theorems To Prove Lines are Parallel
Given
Transitive
Property of
Congruence
AD ІІ BC
Alternate Interior
Angles are congruent

9. Using Theorems to Prove Lines are Parallel
What relationship do we have with angles?
They must be congruent if the two lines are parallel
x = 6

10. 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°

11. 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

12. 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.

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