Transcript Exterior Angles - Nutley Schools

Practice Open-Ended (10 mins)
Discounts & Sales Tax
Sports Authority is having a sale. Every item in the store is discounted,
however the discounts vary throughout the store!
1.) A jacket in the women’s clothing department is
regularly priced at $60 and is on sale for $42.
Determine the percent discount rate for this item.
2.) Find the total cost for a Nike tennis racket that is
regularly priced at $125 and is on sale for 15% off.
(*include a 6% sales tax.)
3.) If all of the sneakers are on sale at the % discount rate in #2, and
the
sales price for a pair of Nike sneakers is $85 (not including
tax),
what was the original price of the sneakers?
Lesson 4
Parallel Lines &
Transversals
Parallel Lines and Transversals
What would you call two lines which do not intersect?
Parallel
Exterior
B
A
Interior
D
A solid arrow placed on
two lines of a diagram
indicate the lines are
parallel.
C
Exterior
The symbol || is used to
indicate parallel lines.
AB || CD
Parallel Lines and Transversals
A slash through the parallel symbol || indicates the lines
are not parallel.
B
AB || CD
A
D
C
Transversal
A line, ray, or segment that intersects 2 or more
COPLANAR lines, rays, or segments.
Exterior
Exterior
Parallel
lines
Interior
Non-Parallel
lines
Interior
Exterior
Exterior
transversal
transversal
Parallel Lines and Transversals
Transversal A transversal is a line which intersects two or more
lines in a plane. The intersected lines do not have to
be parallel.
j
k
m
t
Lines j, k, and m are
intersected by line t.
Therefore, line t is a
transversal of lines j,
k, and m.
INTERIOR
–The space INSIDE the 2 lines
interior
EXTERIOR
-The space OUTSIDE the 2 lines
exterior
exterior
Special Angle Relationships
Interior Angles
Exterior
Interior
Exterior
1
3 4
2
<3 & <6 are Alternate Interior angles
<4 & <5 are Alternate Interior angles
<3 & <5 are Same Side Interior angles
<4 & <6 are Same Side Interior angles
5 6
7 8
Exterior Angles
<1 & <8 are Alternate Exterior angles
<2 & <7 are Alternate Exterior angles
<1 & <7 are Same Side Exterior angles
<2 & <8 are Same Side Exterior angles
Special Angle Relationships
WHEN THE LINES ARE PARALLEL
Exterior
1
3
Interior
5 6
7 8
2
4
Exterior
If the lines are not
parallel, these angle
relationships DO NOT
EXIST.
♥Alternate Interior Angles
are CONGRUENT
♥Alternate Exterior Angles are
CONGRUENT
♥Same Side Interior Angles are
SUPPLEMENTARY
♥Same Side Exterior Angles are
SUPPLEMENTARY
Corresponding Angles & Consecutive
Angles
Corresponding Angles: Two angles that occupy
corresponding positions.
 2   6,  1   5,  3   7,  4   8
Exterior
1
3
2
4
Interior
5 6
7 8 Exterior
Corresponding Angles
When two parallel lines are cut by a transversal, pairs of corresponding
angles are formed.
L
Line L
GPB = PQE
G
A
D
P
B
Q
E
F
Line M
Line N
GPA = PQD
BPQ = EQF
APQ = DQF
Four pairs of corresponding angles are formed.
Corresponding pairs of angles are congruent.
Same Side
Interior/Exterior Angles
Same Side Interior Angles: Two angles that lie between parallel
lines on the same sides of the transversal.
m3 +m5 = 180º, m4 +m6 = 180º
Same Side Exterior Angles: Two angles that lie outside parallel
lines on the same sides of the transversal.
Exterior
1 2
m1 +m7 = 180º, m2 +m8 = 180º
3 4
Interior
5 6
7 8 Exterior
Interior Angles
The angles that lie in the area between the two parallel lines that are
cut by a transversal, are called interior angles.
L
G
A 1200
Line L
Exterior
P
1200
600
D
B
600
F
Line N
APQ + DQP = 1800
Interior
E
Q
Line M
BPQ + EQP = 1800
Exterior
interior
eachside
pairofadd
to 1800.
AThe
pairmeasures
of interiorofangles
lieangles
on theinsame
theup
transversal.
Alternate Interior/Exterior Angles
• Alternate Interior Angles: Two angles that lie between
parallel lines on opposite sides of the transversal (but not a
 3   6,  4   5
linear pair).
Alternate Exterior Angles: Two angles that lie outside parallel
lines on opposite sides of the transversal.
 2   7,  1   8
1 2 Exterior
3 4
Interior
5
7
6
8
Exterior
Alternate Interior Angles
Alternate angles are formed on opposite sides of the transversal and
at different intersecting points.
L
G
A
D
Line L
P
B
Q
E
Line M
Line N
BPQ = DQP
APQ = EQP
F
Two pairs of alternate angles are formed.
Pairs of alternate angles are congruent.
Let’s Practice
120° 1
60° 3
120° 5
7
60°
2 60°
4 120°
6 60°
8 120°
m<1=120°
Find all the remaining angle
measures.
Another practice problem
40°
180-(40+60)= 80°
60°
80°
100°
80°
80°
100°
40°
60°
60°
120°
120°
60°
Find all the missing
angle measures,
and name the
postulate or
theorem that gives
us permission to
make our
statements.
Name the pairs of the following angles formed by a transversal.
GG
G
AA
500
Line
Line
Line LL
L
P P
BBB
1300
D
DD
Q
Q
Q
EEE
FFF
Line
Line
Line
MM M
Line
Line
N
Line
NN
Department Store
A department store is divided into two sections, electronics and furniture. Each section offers a discount rate;
items in the same section sell at the same discount rate, but not necessarily at the same price.
A.) One of the items in the electronics section has an original price $120 and a sale price of $102. One of the
items in the furniture section has an original price of $60 and a sale price of $48. Determine the
(percent) discount rate in the electronics section and the (percent) discount rate in the furniture section.
Show your work.
B.) Using the discount rate found in part A, find the total amount, including a 6% sales tax, that Andrew paid
for an electric item and a furniture item if the original price of each of these items $200. Show your
work.
C.) Andrew plans to buy an office lamp from the furniture section and a laptop computer from the electronic
section of this department store. The original price of the laptop computer is $1,350. The original price
of the office lamp is $89. Andrew is thinking of two methods to find the total amount he will save (not
including the tax). The two methods are stated below:
Method I: Find the discount on the laptop and find the discount on the lamp.
Find the sum of the two discounts
Method II: Find the sum of the original prices of the two items.
Find the average of the discount rates from part A
Use the average rate to find the discount on the sum.
Would Andrew’s results be the same using both methods? Show your work to explain your answer.