3'3 ll Lines

1
3.3 ll Lines Transversals

• p. 143

2
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
3
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
4
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
5
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
6
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
7
Thm 3.7 - ? 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
8
Proof of ? transversal thm

• Statements
• l ??m, t ? l
• ?1??2
• m?1m?2
• ?1 is a rt. ?
• m?190o
• 90om?2
• ?2 is a rt. ?
• t ?m

• Reasons
• Given
• Corresp. ?s post.
• Def of ? ?s
• Def of ? lines
• Def of rt. ?
• Substitution prop
• Def of rt. ?
• Def of ? lines

9

• Ex Find
• m?1
• m?2
• m?3
• m?4
• m?5
• m?6
• x

m?155o m?2125o m?355o m?4125o m?555o m?6125o
x40o
1
125o 2
3
5
4 6
x15o
10
Assignment