1. 3.3 Parallel Lines & Transversals
Geometry

2. Standard/Objectives:
Standard 3: Students will learn and apply geometric concepts.
Objectives:
Prove and use results about parallel lines and transversals.
Use properties of parallel lines.

3. Post. 15 – Corresponding s Post.
If 2  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

4. Thm 3.4 – Alt. Int. s Thm.
If 2  lines are cut by a transversal, then the pairs of alternate interior s are .
i.e. If l m, then 12. 1 2 l m

5. Proof of Alt. Int. s Thm. Statements l m 3  2 1  3 1  2
Reasons
Given
Corresponding s post.
Vert. s Thm
  is transitive 3 1 2 l m

6. Thm 3.5 – Consecutive Int. s thm
If 2  lines are cut by a transversal, then the pairs of consecutive int. s are supplementary.
i.e. If l m, then 1 & 2 are supp. l m 1 2

7. Thm 3.6 – Alt. Ext. s Thm.
If 2  lines are cut by a transversal, then the pairs of alternate exterior s are .
i.e. If l m, then 12.
l m 1 2

8. Thm  Transversal Thm.
If a transversal is  to one of 2  lines, then it is  to the other.
i.e. If l m, & t  l, then t m.
** 1 & 2 added for proof purposes. t 1 2 l m

9. Proof of  transversal thm
Statements
l m, t  l
12
m1=m2
1 is a rt. 
m1=90o
90o=m2
2 is a rt. 
t m
Reasons
Given
Corresp. s post.
Def of  s
Def of  lines
Def of rt. 
Substitution prop =

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

11. 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