Section 3.5
Properties of Parallel
Lines
Transversal
 Is
a line that intersects two or more
coplanar lines at different points.
 Angles formed:




Corresponding angles
Alternate interior angles
Alternate exterior angles
Consecutive interior angles
corresponding
<1 and <5
<4 and <8
<3 and <7
<2 and <6
Alt interior
<3 and <5
<2 and <8
Consecutive interior angles
<2 and <5
<3 and <8
Alt exterior
<1 and <7
<4 and <6
Using properties of Parallel
Lines
 Postulate
Postulate

15: Corresponding Angles
If two parallel lines are cut by a transversal,
then the pairs of corresponding angles are
congruent.
Theorem 3.6
Alternate Interior Angles Theorem
 If
two parallel lines are cut by a
transversal, then the pairs of alternate
interior angles are congruent.
Given: m ││n
Prove: <1 ≌ <2
Statements
1. m││n
2. <3 and <1 are
vertical <‘s
3. <3 ≌ <1
4. <3 ≌ <2
5. <1 ≌ <2
Reasons
1. given
2. def of vert <‘s
3. vertical <‘s thm
4. 2 lines ll corr <‘s
are ≌
5. transitive prop
Theorems:

Thm 3.7: Consecutive Interior Angles Theorem
 If
two parallel lines are cut by a transversal, then
the pairs of consecutive interior angles are
supplementary

Thm 3.8: Alternate Exterior Angles Theorem

If two parallel lines are cut by a transversal, then
the pairs of alternate exterior angles are
congruent
 Thm

3.9: Perpendicular Transversal Theorem
If transversal is perpendicular to one of two
parallel lines, then it is perp to the second.
Parallel Lines and Transversals
Example
Given that m5 = 65°, find
each measure. Tell which
postulate or theorem you
used to find each one.

a.
m6
b.
m7
q
p
9
6
7
m8
c.
d. 9
m
5
8
Parallel Lines and Transversals
 Example

How many other angles have a measure of
100°?
AB || CD
AC || BD
B
A
100°
D
C
Parallel Lines and Transversals
 Example

Use properties of parallel lines to find the
value of x.
(x – 8)°
72°
Parallel Lines and Transversals
 Example

Find the value of x.
x°
70°
(x – 20)°