1.1 warm-up
You pay a $5 processing fee to order tickets
no matter how many tickets you order.
Each ticket costs $18. Which expression
best represents the total cost of ordering
n tickets ?
a. 18n+5
b. 18-n-5
c. 18(n+5)
d. 18(n-5)
4
Pardekooper
Lets look at some new terms.
•Transversal is a line that intersects two coplanar lines at
two distinct points.
Pardekooper
Lets look at the parts.
Alternate interior angles
1 and 2, 3 and 4
1 3
4
2
Pardekooper
Lets look at the parts.
Same-side interior angles
1 and 4, 2 and 3
1
3
4
2
Pardekooper
Lets look at some new terms.
Corresponding angles
1 and 7, 2 and 6,
3 and 8, 4 and 5
5
6
1 3
4
2
7
8
Pardekooper
What if the two lines are
parallel ?
6
5
1
3
4
2
7
8
•Corresponding Angles Postulate
If a transversal intersects two
parallel lines, then corresponding
angles are congruent.
m1 m7
m3  m8
m2  m 6
m4  m5
Pardekooper
What if the two lines are
parallel ?
1
3
4
2
•Alternate Interior Angles Theorem
If a transversal intersects two
parallel lines, then alternate interior
angles are congruent.
m1 m2
m3  m 4
Pardekooper
What if the two lines are
parallel ?
1
3
4
2
•Same-Side Interior Angles Theorem
If a transversal intersects two
parallel lines, then same-side
angles are supplementary.
m1 m4 = 1800
m2  m 3 = 1800
Pardekooper
Lets try some angles.
5
4
1
6
3
2
Classify the following pairs of angles:
1and 2
corresponding ’s
3 and 4
alternate interior ’s
5 and 6
corresponding ’s
Pardekooper
Lets work a problem.
l1
l1 || l2
8
7
l2
l3 || l4
5
6
500 2
4
3
1
l3
l4
Find the following degrees for the angles
and tell the reason:
m1= 500
corresponding ’s
m3= 1300
m4= 1300
same-side ’s
vertical ’s
m5= 500 alternate interior ’s
m2= 1300 same-side ’s
Pardekooper
Lets try just one more
problem.
500
x0
y0
700
Parallel lines
mx= 700
corresponding ’s
mx +500+my=1800
straight  +
700 +500+my=1800
substitution
1200+my=1800
1200-1200+my=1800 -1200
my=600
combine terms
subtraction
combine terms
Pardekooper
Pardekooper
3.1 Properties of Parallel Lines
3
Classify the following pairs of angles.
1.
1 and 2 ____________________
2.
3 and 4 ____________________
3.
5 and 6 ____________________
4.
7 and 8_____________________
5.
9 and 10 ___________________
6.
11 and 12 __________________
1
5 2
4
6
9 11
10 7
12 8
State the reason for the following:
Statements
Reasons
7.
a || b
given
8.
3 and 2 are supplementary
________________________
9.
c || d
given
10
1 and 2 are supplementary
________________________
11.
13
________________________
2x0
y0
(y-50)0
12.
Find x.
13.
Find y
a
1
b
2
3
4
c
d