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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
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