Download Day 1 - Section 3.1 Notes

Definition – coplanar lines
that do not intersect
Examples:
AB
A
B
CD
C
D
Symbol for
Parallel -
Segments and rays can be parallel as well.
J
M
Example:
K
KJ
L
Be Careful! Just because
two segments do not
intersect, does not make
them parallel. Segments
are only parallel if the lines
that contain the segments A
are parallel.
LM
B
C
D
Definition – noncoplanar
lines that are neither
parallel nor intersecting.
Example
Definition – planes that do
not intersect.
G
Examples:
GFDE
HCBA
GHAE
DBCF
Example
E
D
H
A
F
C
B
…If they do not intersect.
G
Examples:
GFDE
GHAE
AB
E
F
D
H
BC
A
C
B
Theorem 3-1: If two parallel
planes are cut by a third plane,
then the lines of intersection
are parallel.
Definition – a line that
intersects two or more
coplanar lines at different
points.
Forms Special Angle Pairs!!
Note: the “two or more
coplanar lines” do NOT
have to be parallel.
When two lines cut by a transversal
several pairs of angles are formed.
3
2
3 and 2 are vertical angles.
Therefore 3 @ 2 because of the
Vertical Angle Theorem
(“Vertical angles are congruent.”)
5 2
m2 + m5 = 180 because of the
Angle Addition Postulate.
2
1
Corresponding Angles
Two angles in corresponding positions
relative to the two lines
3
1
Alternate Interior Angles
Two non-adjacent interior angles on opposite
sides of the transversal
5
4
Alternate Exterior Angles
Two non-adjacent exterior angles on
opposite sides of the transversal.
1
6
Same Side Interior Angles
Two interior angles on the same side
of the transversal.
5
8
Same Side Exterior Angles
Two exterior angles on the same side of the
transversal.
5 2
3 6
7 1
8 4