The document defines and provides examples of parallel lines, perpendicular lines, skew lines, parallel planes, transversals, and the angle properties that exist when lines are cut by a transversal, including corresponding angles, alternate interior angles, alternate exterior angles, and consecutive interior angles. It states that corresponding angles, alternate interior angles, and alternate exterior angles of parallel lines cut by a transversal are congruent, while consecutive interior angles and consecutive exterior angles are supplementary.
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1.4.1 Parallel Lines and 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
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 congruent.of parallel lines are congruent.of parallel lines are congruent.of parallel lines are congruent.
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 congruent.of parallel lines are congruent.of parallel lines are congruent.of parallel lines are congruent.
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 congruent.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 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 supplementary.supplementary.supplementary.supplementary.
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
ConsecutiveConsecutiveConsecutiveConsecutive exterior anglesexterior anglesexterior anglesexterior angles of parallel lines areof parallel lines areof parallel lines areof 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
1 2
3 8
4 5
6 7
Examples