1. Obj. 12 Parallel Lines
The student is able to (I can):
• Identify parallel lines, perpendicular lines, skew lines, and
parallel planes
• Identify• Identify
— Transversals
— Corresponding angles
— Alternate Interior Angles
— Alternate Exterior Angles
— Same-side Interior Angles

2. Parallel Lines
Perpendicular
Coplanar lines that do not intersect
Two coplanar lines that intersect at right
m
n
m n
Perpendicular
Lines
Two coplanar lines that intersect at right
angles (90˚)
f
g
f ⊥ g

3. Skew Lines
Parallel Planes
Noncoplanar lines that do not intersect
Planes that do not intersectParallel Planes Planes that do not intersect
RRRR
SSSS
Plane R Plane S

4. transversal A line that intersects two coplanar lines at
two different points
r
s
t

5. corresponding
angles
Lie on the same side of the transversal t,
on the same sides of lines r and s
Example: ∠1 and ∠5
1 2
r t
87
65
4
3
1 2
s

6. alternate
interior angles
Nonadjacent angles that lie on opposite
sides of the transversal t, between lines r
and s
Example: ∠3 and ∠6
1 2
r
t
87
65
43
1 2
s
interior

7. alternate
exterior angles
Lie on opposite sides of the transversal t,
outside lines r and s
Example: ∠1 and ∠8
1 2
r texterior
87
65
43
1 2
s
exterior

8. same-side
interior angles
Lie on the same side of the transversal t,
between the lines r and s
Example: ∠3 and ∠5
3
1
2
r t
87
65
43
2
s
interior

9. transversal
Corresponding angles are congruentCorresponding angles are congruent
87 6
5
4
3
1
2
∠1 ≅ ∠5
∠2 ≅ ∠6
∠3 ≅ ∠7
∠4 ≅ ∠8

10. Alternate interior angles are congruent
Alternate exterior angles are congruent
8
7 6
5
4
3
1
2
∠2 ≅ ∠7
∠4 ≅ ∠5
Alternate exterior angles are congruent
8
7
6
5
4
3
1
2
∠1 ≅ ∠8
∠4 ≅ ∠5

11. Same-side interior angles are
supplementary.
87
65
43
1 2
87
m∠3 + m∠5 = 180˚
m∠4 + m∠6 = 180˚

12. 1. Find the measures of the
numbered angles
2. List each angle pair
corresponding angles
∠1 & ∠4; ∠2 & ∠5;
∠3 & ∠6; ∠8 & ∠7
1 2
3 125˚
(8)
Practice
m∠1 = 125˚; m∠2 = 55˚;
m∠3 = 55˚; m∠4 = 125˚;
m∠5 = 55˚; m∠6 = 55˚;
m∠7 = 125˚
∠3 & ∠6; ∠8 & ∠7
alt. interior angles
∠3 & ∠5; ∠8 & ∠4
alt. exterior angles
∠1 & ∠7; ∠2 & ∠6
same-side interior angles
∠3 & ∠4; ∠8 & ∠5
4 5
6 7