1. 3.3 Parallel Lines & Transversals

2. Postulate 16 – Corresponding Angles Postulate
If two  lines are cut by a transversal, then the pairs of corresponding s are .
i.e. If l m, then 12. 1 2 l m

3. Section 3.3
Prove Lines are Parallel
Theorems
Theorem 3.4: Alternate Interior Angles Converse
Theorem 3.5: Alternate Exterior Angles Converse
Theorem 3.6: Consecutive Int. Angles Converse
If alternate interior angles are congruent, then the lines are parallel.
If alternate exterior angles are congruent, then the lines are parallel.
If consecutive interior angles are supplementary, then the lines are parallel.

4. Apply the Corresponding Angles Converse
EXAMPLE 1
Apply the Corresponding Angles Converse
Find the value of x that makes m n.
If corr s , then m n .
Set angles = to each other.
(3x + 5)o
= 65o
Corr. Angles Converse 3x
= 60
Subtract 5 x
= 20
Divide by 3

5. GUIDED PRACTICE
for Example 1
Is there enough information in the diagram to conclude that m n? Explain.
75o
Yes, the supplement to 105o is 75o , making corr. angles are congruent , so m n.

6. Proving lines parallel
EXAMPLE 2
Proving lines parallel
Given the information, state the postulate or theorem that proves lines a and b are parallel?
a. 1  5
b. 2  5
c. m 2  m = 180°
d.  3 
Is it possible to prove a // b if 1  ? Explain.
Alt. Ext. Angles Converse
Corr. Angles Converse
Consec. Int. Angles Converse
Alt. Int. Angles Converse
No, angles would need to be supplementary

7. GUIDED PRACTICE
for Example 2
Can you prove that lines a and b are parallel? Explain why or why not.
Yes; Alt. Ext. Angles Converse.

8. GUIDED PRACTICE
for Example 2
Can you prove that lines a and b are parallel? Explain why or why not.
Yes; Corr. Angles Converse.

9. GUIDED PRACTICE
for Example 2
Can you prove that lines a and b are parallel? Explain why or why not.

10. Prove the Alternate Interior Angles Converse
EXAMPLE 3
Prove the Alternate Interior Angles Converse
Prove that if alternate interior angles are congruent, then the lines are parallel.
∠4  ∠5
GIVEN :
PROVE :
g // h
STATEMENTS
REASONS 1.
∠4  ∠5 1.
Given 2.
∠1  ∠4 2.
Vertical ∠s Congruent 3.
∠1  ∠5 3.
Transitive Prop.
g // h 4. 4.
Corr. Angles Converse

11. Section 3.3
Transitive Property of Parallel Lines
Theorem
Theorem 3.7: Transitive Property of Parallel Lines
If 2 lines are parallel to the same line, then they are parallel to each other.
If and ,
then

12. Ex: Find: m1= m2= m3= m4= m5= m6= x=
125o 2 3 5
x+15o

13. Ex: Find: m1=55° m2=125° m3=55° m4=125° m5=55° m6=125° x=40°
125o 2 3 5
x+15o

14. Assignment
Handout found on