Transcript 3.5 Using Properties of Parallel Lines

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.
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3=45°,
m4=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 ║.