3.3 Parallel Lines &

Transversals

GeometryPresented by Mrs. Spitz

Fall 2005

Standard/Objectives:

Standard 3: Students will learn and apply geometric concepts.

Objectives:

1. Prove and use results about parallel lines and transversals.

2. Use properties of parallel lines.

Assignment

• pp. 146 -147 #1-27

• Quiz after this section next class meeting . . . don’t miss it. There is another quiz after 3.5.

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 12.

l

m

1

2

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 12.

l

m

1

2

Proof of Alt. Int. s Thm.Statements

1. l m

2. 3 2

3. 1 3

4. 1 2

Reasons

1. Given

2. Corresponding s post.

3. Vert. s Thm

4. is transitive

l

m

1

2

3

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

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 12.

l m

1

2

• 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.

1

2

Thm 3.7 - Transversal Thm.

l

m

t

Proof of transversal thmStatements

1. l m, t l 2. 12

3. m1=m2

4. 1 is a rt. 5. m1=90o

6. 90o=m2

7. 2 is a rt. 8. t m

Reasons

1. Given

2. Corresp. s post.

3. Def of s

4. Def of lines

5. Def of rt. 6. Substitution prop =

7. Def of rt. 8. Def of lines

Ex: Find:

m1=

m2=

m3=

m4=

m5=

m6=

x=

125o 21

3

4 6

5

x+15o

Ex: Find:

m1=55°

m2=125°

m3=55°

m4=125°

m5=55°

m6=125°

x=40°

125o 21

3

4 6

5

x+15o