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Parallel Lines ;)
Two lines that do not intersect
are either parallel or skew.
Parallel Lines (II lines) are
coplanar lines that do not
intersect.
Skew Lines are non
coplanar lines. Therefore,
they are neither parallel
nor intersecting.
Parallel Segments/Rays
Segments and rays contained in parallel lines
are also called parallel.
If two segments do not have an intersection
point, but are contained in intersecting lines,
we do not call the segments parallel.
Parallel Planes
Two planes that do not intersect are
called parallel planes.
A line and a plane are parallel if
they do not intersect.
Exercises!
Exercises!
Exercises!
Exercises!
Exercises!
Theorem: If two parallel planes are cut by a third plane, then the
lines of intersection are parallel.
Given: Plane A ‖ Plane B
Plane A intersects plane C in line x
Plane B intersects plane C in line y
Prove: line x ‖ line y
Statement
Reason
Transversal
A line that intersects two or more
coplanar lines at different points
1
4
5
8
6
7
2
3
Angles Formed by Two Lines
and a Transversal
1
4
5
8
6
2
1) Corresponding angles
(corr <s) – two angles that
have corresponding positions
relative to the two lines.
3
2) Alternate interior angles
(alt. int. <s) – two nonadjacent
interior angles on opposite
sides of the transversal.
7
3) Same-side Interior (SSI <s)
– two interior angles on the
same side of the transversal.
Learning Log Summary
LT 1 - I can classify pairs of angles and
lines using appropriate vocabulary.
Parallel and skew lines are different because…
Pairs of angles formed when two lines are
intersected by a transversal are…
Closure
Homework
pg. 76 ~ 1-39 (odd)
Theorem 3-9
Through a point outside a line, there is exactly one line
perpendicular to the given line.
Group Task
Prove one of the relationships that
exist among angles formed when
parallel lines are cut by a transversal.
•
What is a transversal?
•
What is the difference between
inductive and deductive
reasoning?
•
Use inductive reasoning to
determine what relationship exists
between corresponding angles.
Corresponding Angle Postulate
If l is parallel to m,
then 1  2 .
Why is this a postulate instead of a theorem?
Group Task
Gallery Walk
Alternate Interior Angle Theorem
If l is parallel to m,
then…
Same Side Interior Angle Theorem
If l is parallel to m,
then…
Theorem 3-4
(Perpendicular Transversal Thm)
If k is parallel to l and k  t,
then…
Learning Log Summary
LT 2 - I can use previous definitions,
properties and postulates to prove angle
relationships when parallel lines are cut by
a transversal.
The postulate necessary to prove other angle
relationships is…
To prove relationships among corr/alt int angles…
If a transversal is perpendicular to one parallel line,
then…
Theorem 3-8
Through a point outside a line, there is exactly one line parallel
to the given line.
Corresponding Angle Postulate
If l is parallel to m,
then corresponding
angles are congruent.
Why is this a postulate instead of a theorem?
Converse to Corresponding
Angle Postulate
If corresponding
angles are congruent,
then l is parallel to m.
Why is this a postulate instead of a theorem?
Converse to Alternate Interior
Angle Theorem Record it on your list!
Converse to Same-Side Interior
Angle Theorem Record it on your list!
Converse to Perpendicular
Transversal Theorem Record it on your list!
Converse to Perpendicular
Transversal Theorem
Learning Log Summary
LT 4 - I can use previous definitions,
properties and postulates to prove that
lines are parallel, given specific
relationships that exist between the angles
formed.
The ways to prove that two lines are parallel…
The angle relationship you establish also establishes
the parallel lines and the transversal because…