Download Geometry 4.5 Class Notes

WARM UP
Look through pages 192-195
 Write down the definitions of

– Transversals
– Interior
– Exterior
– Alternate Interior Angles
– Alternate Exterior Angles
– Corresponding Angles
4.5 Parallel lines
Obj:
recognize
planes,
Recognize transversals,
 identify the pairs of angles
formed by a transversal,
 recognize parallel lines.
Plane:
•A surface with any two points
connected by a line. There
must be at least one point not
on the line.
•Has only two dimensions,
length and width (infinite)
•Has no thickness
y
x
Plane m
m
Coplanar:
• Points that lie on the same
plane (like collinear)
Non-coplanar:
• points that do not lie on the
same plane
Transversals:
• A line that intersects two
coplanar lines in two distinct
points. Not always parallel.
•Parts of a transversal:
•Exterior region
•Interior region
•Exterior region
Transversals angles:
• alternate interior angles, angles
on opposite sides of the
transversal in the interior region
• alternate exterior angles, angles
on opposite sides if the
transversal in the exterior region
• corresponding angles: angles
in the same position in relation
to the transversal
5
1
2
6
3
7
4
8
Name the alternate interior
angles.
Name the alternate exterior
angles.
Name the corresponding angles.
Given: lines n and m are parallel cut
by transversal k
k
n
m
1
2
3
4
5
6
7
8
When the two lines cut by the
transversal are parallel,
certain angles are congruent!
k
n
m
1
2
3
4
5
6
8
Alternate interior angles are congruent
Alternate exterior angles are congruent
Corresponding angles are congruent
k
n
m
1
2
3
4
5
6
8
Name the alternate interior angles
Name the alternate exterior angles
Name the corresponding angles
What other angles are congruent???
Notice: if you know one angle in a set of
transversal lines where two of the lines are
parallel, you know all eight angles.
Given: <1 = 45degrees, name the other
angles.
k
n
m
1
2
3
4
5
6
8
Parallel lines:
• two coplanar lines that do not
intersect. (equidistance apart)
• symbol ll or on lines > >
• segments and rays can also be
parallel
• to be parallel, the lines MUST
BE COPLANAR!
Skew lines:
• Lines that never touch
• aren’t coplanar or parallel!