Download 3.2 - Parallel Lines and Transversals.notebook

3.2 ­ Parallel Lines and Transversals.notebook
Bellringer: Mon. Jan 9th January 09, 2017
Mental Floss: Tues. Jan 10th If a||b, find all missing angle measures.
Find the values of x and y.
a
b
3.2 ­ Parallel Lines and Related Angles
1 2 Transversal = A line that intersects two coplanar lines at two distinct points.
Corresponding Angles
1.) On the same side of the transversal
Pod 1 2 3 4 3 4 Two coplanar lines
Both in upper right, just different "pods" Pod 5 7 2.) Both angles in the same location, just a different "pod"
6 5
6 8
7 8 Examples:
1
3.2 ­ Parallel Lines and Transversals.notebook
Alternate Interior Angles (AIA) 1 2 3 5
4 1 2 3 4 2.) Interior ­ Both angles in between the two lines
6 Examples:
Alternate Exterior Angles (AEA) 1 2 Same Side Interior Angles (SSI)
1.) Alternate ­ On opposite sides of the transversal
7 8 3 4 January 09, 2017
5
6 7 8 6 7 8 2.) Interior ­ Both angles in between the two lines
Examples:
Same Side Exterior Angles (SSE)
1.) Alternate ­ On opposite sides of the transversal
1 2 3 4 2.) Exterior ­ Both angles outside the two lines
5
5
1.) Same Side ­ On the same side of the transversal.
1.) Same Side ­ On the same side of the transversal
2.) Exterior ­ Both angles outside the two lines
6 7 8 Examples:
Examples:
2
3.2 ­ Parallel Lines and Transversals.notebook
January 09, 2017
Homework • 3.2 p.135 #2­12,14,18,23,24,26
Name
Corresponding Angles
Name
Examples
Description
Facts
Alternate Interior Angles
Alternate Exterior Angles
Examples
Description
­Same location, different "pod"
­Same side transversal
­Opposite sides of the transversal
­Both angles between the || lines
­Opposite sides of the transversal
­Both angles outside the || lines
Same Side Interior Angles
­Same side of the transversal
Same Side Exterior Angles
­Same side of the transversal
­Both angles between the || lines
­Both angles outside the || lines
Facts
If lines || ,
then angles ≅
If lines || ,
then angles ≅
If lines || ,
then angles ≅
If lines || ,
then angles supp.
If lines || ,
then angles supp.
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3.2 ­ Parallel Lines and Transversals.notebook
Parallel Theorems (Part 2)
January 09, 2017
Mental Floss: Thurs. Nov 19th Is m||n? Justify your answer.
If || Lines, Then
m
n
If
(Given)
Then
(Proving)
4
3.2 ­ Parallel Lines and Transversals.notebook
January 09, 2017
Thm: If two coplanar lines are both perpendicular to a third line, then they are parallel.
n
m
Crook Problems
Parallel Lines ­ Extension
a b m n 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 5
3.2 ­ Parallel Lines and Transversals.notebook
H
F
Parallel Theorems
January 09, 2017
Given:
midpoint
Prove:
O
X
A
6