Parthenon
Athens
Dallas City Hall
I.M. Pei
Havasu Falls
I.M. Pei
Parallel Lines and Planes
Lesson 3.2 Classroom Exercises
Mr. Sabia’s Favorite Theorem
Vertical angles are congruent.
VA are 
X marks the spot.
Mr. Sabia’s 2nd Favorite Theorem
Linear pairs are supplementary.
Lp’s are suppl.
a
b
m  a  m  b 180
Mr. Sabia’s Third Favorite Theorem
If 2 lines are //, then the Alternate Interior angles are congruent.
AIA are 
If two lines are parallel….
The corresponding angles are congruent.
The alternate interior angles are congruent.
The alternate exterior angles are congruent.
The same-side interior angles are supplementary.
The same-side exterior angles are supplementary.
T
1
1 2
What do the
arrowheads in
the diagram
tell you?
L // P
3
4
K
L
5 6
7 8
P
T
2 State the postulate
or theorem that
justifies each
statement.
1   5
K
1 2
3
4
L
5 6
7 8
If 2 lines are parallel and cut by a transversal,
Then the corresponding angles are congruent.
P
T
3 State the postulate
or theorem that
justifies each
statement.
3 6
K
1 2
3
4
L
5 6
7 8
If 2 lines are parallel and cut by a transversal,
Then the alternate interior angles are congruent.
P
T
4 State the postulate
or theorem that
justifies each
statement.
K
1 2
3
4
L
5 6
m  4  m  6 180
7 8
If 2 lines are parallel and cut by a transversal,
Then the same-side interior angles are supplementary.
P
T
5 State the postulate
or theorem that
justifies each
statement.
m  4  m 8
K
1 2
3
4
L
5 6
7 8
If 2 lines are parallel and cut by a transversal,
Then the corresponding angles are congruent.
P
T
6 State the postulate
or theorem that
justifies each
statement.
m  4  m 5
K
1 2
3
4
L
5 6
7 8
If 2 lines are parallel and cut by a transversal,
Then the alternate interior angles are congruent.
P
T
7 State the postulate
or theorem that
justifies each
statement.
6  7
1 2
3
4
K
L
5 6
7 8
Vertical angles are congruent.
P
T
8 State the postulate
or theorem that
justifies each
statement.
K P
1 2
3
4
K
L
5 6
7 8
If a line is perpendicular to on of
two parallel lines, then it is
perpendicular to the other.
P
T
9 State the postulate
or theorem that
justifies each
statement.
K
1 2
3
4
L
5 6
7 8
 3 is complementary to  5
If 2 lines are parallel and cut by a transversal,
Then the same-side interior angles are supplementary.
P
T
10 State the postulate
or theorem that
justifies each
statement.
If the measure of angle 1 is
130, what are the measures
of the other angles?
1300 1 500
2
5003 4 1300
K
L
1300
0
50
5 6
50
0 7 81300
P
T
11 State the postulate
or theorem that
justifies each
statement.
If the measure of angle 1 is
x, what are the measures of
the other angles?
x
1 2
180-x
180-x3 4 x
x
5 6
7 8x
180-x
K
L
180-x
P
T
12 State the postulate
or theorem that
justifies each
statement.
If m  4  2m  3,
then find m  6.
x + 2x = 180
3x = 180
x = 60
1 2
3
x
5 6
7 8
4
K
L
2x
60, AIA
P
13 State the postulate
or theorem that
justifies each
statement.
If m  5  m  6  20,
then find m  1.
x + 20
T
CA
1 2
3
4
5 6
x
7 8
x + x + 20 = 180
2x + 20 = 180
2x = 160
x = 80
m 1 x  20
m1100
K
L
P
C’est fini.
Good day and good luck.