Postulate or
Theorem
Corresponding
Angles Postulate
Definition
Diagram
If two parallel lines are cut by a transversal,
then the pairs of corresponding
angles are congruent.
Corresponding
Angles Converse
Postulate
If two lines are cut by a transversal so that
corresponding angles are congruent, then the
Alternate Interior
Angles Converse
Theorem
If two lines are cut by a transversal so that
alternate interior are congruent, then the
k
j
If two lines are cut by a transversal so that
consecutive interior angles are supplementary,
then the lines are parallel.
k
j
If two lines are cut by a transversal so that
alternate exterior angles are congruent, then
the lines are parallel.
k
j
Consecutive Interior
Angles Converse
Theorem
Alternate Exterior
Angles Converse
Theorem
lines are parallel.
lines are parallel.
____________________
If k || j, then
1
2
t
k
j
State the postulate or theorem that supports each conclusion.
1. Given: a || b
Conclusion: ∠ 2 ≅ ∠ 7
t
k
j
If ∠1 ≅ ∠2 ,
then
1
2
t
If ∠1 ≅ ∠2 ,
then
1
2
t
2
If m∠1 + m∠2
=180, then
1
t
2
If ∠1 ≅ ∠2 ,
then
1
a
b
5
2. Given: m ∠ 4 + m ∠ 7 = 180 ____________________
Conclusion: a ll b
3. Given: ∠ 4 ≅ ∠ 5
Conclusion: a ll b
1
3
2
7
6
8
4
____________________
Find the values of x and y. Explain your reasoning by stating the proper theorem or
postulate.
4.
5.
130
65 y
x
y
x
x=
y=
_____________________
_____________________
x=
y=
_____________________
_____________________
6.
y
x
80
x=
y=
_____________________
_____________________
Find the value of x so that n | | m . State the theorem or postulate that justifies
your solution.
7.
5x
n
8.
m
m
n
5x+23
9.
7x+13
n
5x-18
m
8x-5
3x+48
x=
x=
x=
_____________________
_____________________
_____________________
Given: a
Prove: x
b and < 1 ≅ < 3
x
y
1
2
y
a
b
4
3
Use the figure where n ll m to complete the following statements.
10. If m ∠ 4 = 20, then m ∠ 7= ________.
11. If m ∠ 5 = 75, then m ∠ 8 = _______.
12. If n ⊥ t, then m ∠ 3 = _______.
m
n
1
2
8 7
13. If m ∠ 1 + m ∠ 3 = 230, then m ∠ 6 = _______.
Transitive property of Parallel Lines
If two lines are parallel to the same line , then they are parallel to each other
3
t
4
6
5