1.4.1 Parallel Lines and Transversals

Identify parallel lines, perpendicular lines, skew lines, and parallel planes.
Identify angles formed by lines and a transversal.

1. Parallel Lines & Transversals
The student is able to (I can):
• Identify parallel lines, perpendicular lines, skew lines, and
parallel planes
• Identify
– Transversals
– Corresponding angles
– Alternate Interior Angles
– Alternate Exterior Angles
– Consecutive Interior Angles

2. parallel parallel parallel parallel lines lines lines lines –coplanar lines that do not intersect
perpendicular perpendicular perpendicular perpendicular lines lines lines lines –two coplanar lines that intersect at right
angles (90˚)
m
n
mmn
f
gf⊥g
⊥means
“perpendicular”
mmeans “parallel”

3. skew skew skew skew lines lines lines lines –noncoplanar lines that do not intersect
parallel parallel parallel parallel planes planes planes planes –planes that do not intersect
R
S
Plane RmPlane S

4. transversal transversal transversal transversal –a line that intersects two coplanar li nes at two
different points
r
s
t

5. corresponding corresponding corresponding corresponding angles angles angles angles–angles that lie on the same side of the
transversal t, on the same sides of lines rand s
Example: ∠1 and ∠5
Corresponding Corresponding Corresponding Corresponding angles angles angles angles of parallel lines are congruent. of parallel lines are congruent. of parallel lines are congruent. of parallel lines are congruent.
8
76
5
4
3
1
2
∠1 ≅∠5 ∠2 ≅∠6 ∠3 ≅∠7 ∠4 ≅∠8
t
s
r

6. alternate interior alternate interior alternate interior alternate interior angles angles angles angles –angles that lie on opposite sides of
the transversal t, between lines r and s
Example: ∠2 and ∠7 or ∠4 and ∠5
Alternate interior angles Alternate interior angles Alternate interior angles Alternate interior angles of parallel lines are con gruent. of parallel lines are congruent. of parallel lines are congruent. of parallel lines are congruent.
r
s
t
interior
8
76
5
4
3
1
2∠2 ≅∠7 ∠4 ≅∠5

7. alternate exterior alternate exterior alternate exterior alternate exterior angles angles angles angles –angles that lie on opposite sides of
the transversal t, outside lines rand s
Example: ∠1 and ∠8
Alternate exterior angles Alternate exterior angles Alternate exterior angles Alternate exterior angles of parallel lines are con gruent. of parallel lines are congruent. of parallel lines are congruent. of parallel lines are congruent.
r
s
t
exterior
exterior
8
7
6
5
4
3
1
2
∠1 ≅∠8 ∠4 ≅∠5

8. consecutive interior consecutive interior consecutive interior consecutive interior angles angles angles angles –angles that lie on the same side
of the transversal t, between the lines rand s.
Example: ∠3 and ∠5
Consecutive Consecutive Consecutive Consecutive interior angles interior angles interior angles interior angles of parallel lines are of parallel lines are of parallel lines are of parallel lines are supplementary. supplementary. supplementary. supplementary.
r
s
t
interior
87
65
43
1 2
m∠3 + m∠5 = 180˚ m∠4 + m∠6 = 180˚

9. consecutive consecutive consecutive consecutive exterior angles exterior angles exterior angles exterior angles –angles that lie on the same side
of the transversal t, outside the lines rand s.
Example: ∠2 and ∠8
Consecutive Consecutive Consecutive Consecutive exterior angles exterior angles exterior angles exterior angles of parallel lines are of parallel lines are of parallel lines are of parallel lines are supplementary. supplementary. supplementary. supplementary.
r
s
t
interior
87
65
43
1 2
m∠1 + m∠7 = 180˚ m∠2 + m∠8 = 180˚

10. 1. Find the measures of the
numbered angles if
m∠8 = 125˚
2. List each angle pair
corresponding angles
alt. interior angles
alt. exterior angles
consecutive interior angles
12
3 8
45
67
Examples

11. 1. Find the measures of the
numbered angles if
m∠8 = 125˚
m∠1 = 125˚; m∠2 = 55˚;
m∠3 = 55˚; m∠4 = 125˚;
m∠5 = 55˚; m∠6 = 55˚;
m∠7 = 125˚
2. List each angle pair
corresponding angles
∠1 & ∠4; ∠2 & ∠5;
∠3 & ∠6; ∠8 & ∠7
alt. interior angles
∠3 & ∠5; ∠8 & ∠4
alt. exterior angles
∠1 & ∠7; ∠2 & ∠6
consecutive interior angles
∠3 & ∠4; ∠8 & ∠5
12
3 8
45
67
Examples