1. Properties of Parallel Lines
Geometry 3.5

2. Goal #1: Angles Formed by a Transversal2 4 3 5 6 7 8
transversal is a line
that intersects two
or more coplanar lines
at different points

3. Angles formed by a Transversal1 2 4 3 5 6 7 8
Corresponding
1 and 5
2 and 6
3 and 7
4 and 8
Consecutive Interior
3 and 5
4 and 6
Alternate Interior
3 and 6
4 and 5
Alternate Exterior
1 and 8
2 and 7

4. Goal #2: Using Properties of Parallel lines3 4 6 5 8 7 1
What do you think the
relationship between the
following angles are?
m3 m6
m4 m5
m1 m8
m2 m7
m1 m5
m2 m6
m3 m7
m4 m8
m3 and m5 are
m4 and m6 are

5. Corresponding Angles Postulate
If two parallel lines are cut by a transversal,
then corresponding angles are congruent. l1 l2 t 2 3 4 6 5 8 7 1
m1 = m5
m2 = m6
m3 = m7
m4 = m8

6. Consecutive Interior Angles Theorem
If two parallel lines are cut by a transversal,
then consecutive interior angles are supplementary. l1 l2 t 2 3 4 6 5 8 7 1
m3 + m5 = 180o
m4 + m6 = 180o

7. Alternate Interior Angles Theorem
If two parallel lines are cut by a transversal,
then alternate interior angles are congruent. l1 l2 t 2 3 4 6 5 8 7 1
m3 = m6
m4 = m5

8. Alternate Exterior Angles Theorem
If two parallel lines are cut by a transversal,
then alternate exterior angles are congruent. l1 l2 t 2 3 4 6 5 8 7 1
m1 = m8
m2 = m7

9. Perpendicular Transversal Theorem
If a transversal is perpendicular to one of two parallel lines,
then it is perpendicular to the second. t
Given: l1 // l2
t  l 1 l1
Therefore,
t  l 2 l2

10. Summary l1 l2 t If l1 // l2 , then, corresponding angles are .3 4 6 5 8 7 1
If l1 // l2 ,
then, corresponding angles are .
alternate interior angles are .
alternate exterior angles are .
consecutive interior angles are supplementary.