Download October 19, 2015 3.1 Pairs of Lines and Angles

October 19, 2015
3.1 Pairs of Lines and Angles
Geometry
3.1 Pairs of Lines & Angles
Essential Question
What does it mean when two line are
parallel, intersecting, coincident, or skew?
October 19, 2015
3.1 Pairs of Lines and Angles
Parallel Lines
Coplanar lines that do not
intersect.
m || n
m
n
Small arrows are used in a diagram
to show lines are parallel.
October 19, 2015
3.1 Pairs of Lines and Angles
Skew Lines
Lines that do not intersect and are not
coplanar. s
r
October 19, 2015
3.1 Pairs of Lines and Angles
Parallel Planes
Planes that don’t intersect.
October 19, 2015
3.1 Pairs of Lines and Angles
Segments and Rays can be
parallel.
B
Sketch the following examples.
AB || CD
D
A
C
MN || OP
M
O
N
P
October 19, 2015
3.1 Pairs of Lines and Angles
Visualization
B
D
AB and ED
Parallel
E
A
AB and EF
Skew
G
AB and BD
Perpendicular
October 19, 2015
F
Think of a
rectangular box.
3.1 Pairs of Lines and Angles
Example 1
Think of each segment in the figure are part of a
line. Identify each pair of lines as parallel, skew
E
or perpendicular.
F
A
Parallel
B
Perpendicular
Perpendicular
Skew
October 19, 2015
G
D
C
3.1 Pairs of Lines and Angles
L
Your turn
M
Q
P
R
N
Name a ...
 Line parallel to
 Line perpendicular to
 Line skew to
 Plane parallel to plane RPL. Plane SNM
October 19, 2015
S
3.1 Pairs of Lines and Angles
Postulate 3.1 Parallel Postulate
If there is a line and a point not on
the line, then there is exactly one
line through the point parallel to
the given line.
October 19, 2015
3.1 Pairs of Lines and Angles
Postulate 3.2 Perpendicular Postulate
If there is a line and a point not on
the line, then there is exactly one
line through the point
perpendicular to the given line.
October 19, 2015
3.1 Pairs of Lines and Angles
Example 2
The given line markings show
how the roads in a town are
related to one another.
 Name a pair of parallel lines.
𝐷𝑀 𝑎𝑛𝑑 𝐹𝐸
 Name a pair of perpendicular
lines.
𝐷𝑀 𝑎𝑛𝑑 𝐵𝐹
 Is
No!
October 19, 2015
3.1 Pairs of Lines and Angles
Transversals
A transversal is a line that intersects
two or more coplanar lines at different
points.
t
Transversal
m
n
October 19, 2015
3.1 Pairs of Lines and Angles
This is not a transversal.
The lines intersect at
only one point.
October 19, 2015
3.1 Pairs of Lines and Angles
Special Angle Pairs
These are identified by their positions relative to
one another. Learn to identify them and name
them. These are listed on page 128 of the text.
1 2
4 3
5 6
8 7
October 19, 2015
3.1 Pairs of Lines and Angles
Corresponding angles
1 & 5
2 & 6
1 2
4 3
3 & 7
4 &  8
5 6
8 7
October 19, 2015
3.1 Pairs of Lines and Angles
Alternate Exterior Angles
1 & 7
2 & 8
1 2
4 3
5 6
8 7
October 19, 2015
3.1 Pairs of Lines and Angles
Alternate Interior Angles
4 & 6
3 & 5
1 2
4 3
5 6
8 7
October 19, 2015
3.1 Pairs of Lines and Angles
Same Side Interior Angles
(Your book calls these
Consecutive Interior Angles. We
will use Same Side Interior.)
4 & 5
3 & 6
1 2
4 3
5 6
8 7
October 19, 2015
3.1 Pairs of Lines and Angles
Abbreviations

Corresponding Angles
– Corr s

Alternate Exterior Angles
– Alt Ext s

Alternate Interior Angles
– Alt Int s

Same Side Interior Angles
– SS Int s
October 19, 2015
3.1 Pairs of Lines and Angles
Example 3
Identify the relationship.
  4 and  10 Alt Ext s
  5 and  8 SS Int s
  8 and  6 Alt Int s
3 4
6 5
7 8
10 9
October 19, 2015
3.1 Pairs of Lines and Angles
Your Turn
Identify the relationship.
  3 and  7 Corr s
  9 and  5 Corr s
  5 and  7 Alt Int s
3 4
6 5
7 8
10 9
October 19, 2015
3.1 Pairs of Lines and Angles
Example 4
Identify all pairs of angles of the given
type.
 Corresponding
 Alternate Interior
 Alternate Exterior
 Same Side Interior
October 19, 2015
3.1 Pairs of Lines and Angles
Example 4
Identify all pairs of angles of the given
type.

Corresponding
 1 &  5,  2 &  6,  3 &  7,
4&8
 Alternate Interior
 2 &  7,  4 &  5

Alternate Exterior
 1 &  8,  3 &  6

Same Side Interior
 2 &  5,  4 &  7
October 19, 2015
3.1 Pairs of Lines and Angles
If these lines
are parallel,
then why do
they appear to
intersect?
Projective Geometry
October 19, 2015
3.1 Pairs of Lines and Angles
Assignment
Pg. 129 #3 – 19 , 24 – 31 ALL
October 19, 2015
3.1 Pairs of Lines and Angles