Properties of Parallel Lines

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Properties of Parallel Lines

• Tutorial 7c

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Angles and Intersecting Lines

• A transversal is a line that intersects two
  coplanar lines at two distinct points.

Line t below is a transversal because it
intersects lines l and m
1
2
l
?1, ?2, ?7, and ?8 are all considered to be
exterior angles.
3
4
?3, ?4, ?5, and ?6 are all considered to be
interior angles.
5
6
m
7
8
t
3
Angles and Intersecting Lines
Alternate Interior angles A pair of interior
angles that lie on alternate sides of the
transversal. ?3 and ?6 ?4 and ?5
Corresponding Angles A pair of angles that lie
on the same side of the transversal yet one lies
on the interior and one lies on the exterior. ?1
and ?5 ?2 and ?6 ?3 and ?7 ?4 and ?8
Same-side Interior angles A pair of interior
angles that lie on the same side of the
transversal. ?3 and ?5 ?4 and ?6
1
2
l
3
4
Alternate-Exterior angles A pair of exterior
angles that lie on the alternate sides of the
transversal. ?1 and ?8 ?2 and ?7
5
6
m
7
8
t
4
Parallel Lines

• Parallel Lines are two or more lines on the same
  plane(coplaner) that do not intersect.

m
n
m n
Line m is parallel to line n. We can write this
using the following symbol
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Corresponding Angles Postulate

• If two parallel lines are cut by a transversal,
  then corresponding angles are congruent.

Corresponding Angles ?1 ? ?5 ?2 ? ?6 ?3 ? ?7 ?4 ?
?8
1
2
l
4
3
5
6
7
8
m
t
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Alternate Interior Angles Theorem

• If two parallel lines are cut by a transversal,
  then alternate interior angles are congruent.

Alternate Interior angles ?3 ? ?6 ?4 ? ?5
1
2
l
4
3
5
6
7
8
m
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Same-Side Interior Angles Theorem

• If two parallel lines are cut by a transversal,
  then the pairs of same-side interior angles are
  supplementary.

1
2
l
4
3
5
6
7
8
m
8
Alternate Exterior Angles Theorem

• If two parallel lines are cut by a transversal,
  then alternate exterior angles are congruent.

Alternate Exterior angles ?1 ? ?8 ?2 ? ?7
1
2
l
4
3
5
6
7
8
m
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• 4. Alternate Interior Angles
• Same-side Interior Angles
• Corresponding Angles

1. Corresponding Angles
2. Alternate Interior Angles
3. Same-side Interior Angles

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Double arrows mean that the lines are parallel.
Click here to check your answers
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Double arrows mean that the lines are parallel.
Same-side Interior Angles x 121 180
x 59
Same-side Interior Angles x 117 180
x 63
Same-side Interior Angles x 74 180 x
106
Same-side Interior Angles x 90 180 x
90
Same-side Interior Angles x 68 180
x 112
Same-side Interior Angles x 109 180
x 71
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Click here to check your answers
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Alternate Interior Angles m?1 60º
Alternate Interior Angles m?1 130º
Alternate Interior Angles m?1 40º
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next lesson