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

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. parallelparallelparallelparallel lineslineslineslines – coplanar lines that do not intersect
perpendicularperpendicularperpendicularperpendicular lineslineslineslines – two coplanar lines that intersect at right
angles (90˚)
m
n
m n
f
g f ⊥ g
⊥ means
“perpendicular”
means “parallel”

3. skewskewskewskew lineslineslineslines – noncoplanar lines that do not intersect
parallelparallelparallelparallel planesplanesplanesplanes – planes that do not intersect
R
S
Plane R Plane S

4. transversaltransversaltransversaltransversal – a line that intersects two coplanar lines at two
different points
r
s
t

5. correspondingcorrespondingcorrespondingcorresponding anglesanglesanglesangles – angles that lie on the same side of the
transversal t, on the same sides of lines r and s
Example: ∠1 and ∠5
CorrespondingCorrespondingCorrespondingCorresponding anglesanglesanglesangles of parallel lines are congruentof parallel lines are congruentof parallel lines are congruentof parallel lines are congruent....
(“If 2 lines , then corr. ∠s ≅”)
87 6
5
4
3
1
2
∠1 ≅ ∠5
∠2 ≅ ∠6
∠3 ≅ ∠7
∠4 ≅ ∠8
t
s
r

6. alternate interioralternate interioralternate interioralternate interior anglesanglesanglesangles – 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 anglesAlternate interior anglesAlternate interior anglesAlternate interior angles of parallel lines are congruentof parallel lines are congruentof parallel lines are congruentof parallel lines are congruent....
(“If 2 lines , then alt. int. ∠s ≅.”)
r
s
t
interior
8
7 6
5
4
3
1
2 ∠2 ≅ ∠7
∠4 ≅ ∠5

7. alternate exterioralternate exterioralternate exterioralternate exterior anglesanglesanglesangles – angles that lie on opposite sides of
the transversal t, outside lines r and s
Example: ∠1 and ∠8
Alternate exterior anglesAlternate exterior anglesAlternate exterior anglesAlternate exterior angles of parallel lines are congruentof parallel lines are congruentof parallel lines are congruentof parallel lines are congruent....
(“If 2 lines , then alt. ext. ∠s ≅.”)
r
s
t
exterior
exterior
8
7
6
5
4
3
1
2
∠1 ≅ ∠8
∠4 ≅ ∠5

8. consecutive interiorconsecutive interiorconsecutive interiorconsecutive interior anglesanglesanglesangles – angles that lie on the same side
of the transversal t, between the lines r and s.
Example: ∠3 and ∠5
ConsecutiveConsecutiveConsecutiveConsecutive interior anglesinterior anglesinterior anglesinterior angles of parallel lines areof parallel lines areof parallel lines areof parallel lines are supplementarysupplementarysupplementarysupplementary....
(“If 2 lines , then cons. int. ∠s supp.”)
r
s
t
interior
87
65
43
1 2
m∠3 + m∠5 = 180˚
m∠4 + m∠6 = 180˚

9. consecutiveconsecutiveconsecutiveconsecutive exterior anglesexterior anglesexterior anglesexterior angles – angles that lie on the same side
of the transversal t, outside the lines r and s.
Example: ∠2 and ∠8
Consecutive exterior angles of parallel lines areConsecutive exterior angles of parallel lines areConsecutive exterior angles of parallel lines areConsecutive exterior angles of parallel lines are supplementarysupplementarysupplementarysupplementary....
(“If 2 lines , then cons. ext. ∠s supp.”)
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
1 2
3 8
4 5
6 7
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
1 2
3 8
4 5
6 7
Examples