Transcript 3.5 Using Properties of Parallel Lines

3.5 Using Properties of
Parallel Lines
Geometry
Ms. Reser
Review Parallel Lines and
Transversal 3.3
Remember if two parallel lines are
cut by a transversal. Then
Corresponding angles are congruent
Alternate Ext angles are congruent
Alternate Int angles are congruent
And consecutive or same side int
angles are supplememntary
Find the value 0f x and y
given the lines are parallel!
Proving lines are parallel
If you are given two lines cut by a transversal and you
want to STATE they are parallel one of the following must
be true!!!! If one of these conditions does not apply you
cannot say they are parallel. These are the converse
statements
Corresponding angles are congruent
Alternate Ext angles are congruent
Alternate Int angles are congruent
And consecutive or same side int angles are supplementary
OR if you know the equation, points or have the line on a
coordinate plane and the slopes are the same you can say
they are parallel!!!
YOU CANNOT SAY THEY ARE PARALLEL BECAUSE
THEY DO NOT INTERSECT!!!! YOU MUST GIVE A VALID
REASON
Standard/Objectives:
Standard 3: Students will learn and apply
geometric concepts.
Objectives:
Use properties of parallel lines in real-life
situations, such as building a CD rack.
Construct parallel lines using a straight
edge and a compass.
To understand how light bends when it
passes through glass or water.
Assignment:
Quiz after this section.
Pg. 159 – Do constructions on this page
“Copying an Angle” and “Parallel Lines.”
Place in your binder under computer/lab
work. In your homework, you are asked
to do constructions on pg. 161 #25-28.
Place these in your binder.
Pgs. 160-162 #1-24, 33-36.
Ex. 1: Proving two lines are
parallel
Lines m, n and k represent three of
the oars of a team of rowers.
Given: m║n and n║k. Prove: m║k.
1
m
n
2
k
3
Proof:
Statements:
1.
2.
3.
4.
5.
6.
m║n
1 ≅ 2
n║k
2 ≅ 3
1 ≅ 3
m║k
Reasons:
1.
2.
3.
4.
5.
6.
Given
Corresponding
Angles Postulate
Given
Corresponding
Angles Postulate
Transitive POC
Corresponding
Angles Converse
Parallel/Perpendicular lines
Theorems
Theorem 3.11: If two lines are
parallel to the same line, then they
are parallel to each other.
p
q
r
If p║q and q║r,
then p║r.
Parallel/Perpendicular lines
Theorems
Theorem 3.12: In a plane, if two
lines are perpendicular to the same
line, then they are parallel to each
other. m
If mp and np, then
n
m║n.
p
Ex. 2: Why steps are parallel
In the diagram at the
right, each step is
parallel to the step
immediately below it
and the bottom step
is parallel to the floor.
Explain why the top
step is parallel to the
floor.
k1
k2
k3
k4
Solution
You are given that k1║ k2 and k2║
k3. By transitivity of parallel lines,
k1║ k3. Since k1║ k3 and k3║ k4, it
follows that k1║ k4. So the top step
is parallel to the floor.
Ex. 3: Building a CD Rack
You are building a CD rack. You
cut the sides, bottom, and top so
that each corner is composed of two
45° angles. Prove that the top and
bottom front edges of the CD rack
are parallel.
Proof:
Given: m1 = 45°, m2 = 45°, m3 =
45°, m = 45°
Prove: BA║CD
B
1
2
A
3
C
4
D
mABC = m1+ m2
Angle Addition Postulate
m1=45°,
m2=45°
Given
m1=45°,
m2=45°
mBCD = m3+ m4
Angle Addition Postulate
Given
mABC = 90°
mBCD = 90°
Substitution Property
Substitution Property
ABC is a
right angle.
BCD is a
right angle.
Definition of Right Angle
Definition of Right Angle
BCCD
BABC
Definition of  lines
Definition of  lines
BACD
In a plane, 2 lines to the same
line are ║.
Constructions:
Do the two constructions on page
159. Label and place in your
binder.
Do Constructions on page 161 #2528. Label and place in your binder.
Reminder:
Quiz 2 will be the next time we
meet. To look at a similar quiz,
check out page 164.