Angles and Parallel Lines

1
Lesson 2-4

• Angles and Parallel Lines

2
Transversal

• Definition A line that intersects two or more
  lines in a plane at different points is called a
  transversal.
• When a transversal t intersects line n and m,
  eight angles of the following types are formed
• Exterior angles
• Interior angles
• Consecutive interior angles
• Alternative exterior angles
• Alternative interior angles
• Corresponding angles

t
m
n
3
Vertical Angles Linear Pair

• Vertical Angles
• Linear Pair

Two angles that are opposite angles. Vertical
angles are congruent.
? 1 ? ? 4, ? 2 ? ? 3, ? 5 ? ? 8, ? 6 ? ? 7
Supplementary angles that form a line (sum 180?)
?1 ?2 , ?2 ?4 , ?4 ?3, ?3 ?1, ?5 ?6,
?6 ?8, ?8 ?7, ?7 ?5
1
2
3
4
5
6
7
8
4
Angles and Parallel Lines

• If two parallel lines are cut by a transversal,
  then the following pairs of angles are congruent.
• Corresponding angles
• Alternate interior angles
• Alternate exterior angles
• If two parallel lines are cut by a transversal,
  then the following pairs of angles are
  supplementary.
• Consecutive interior angles
• Consecutive exterior angles

Continued..
5
Corresponding Angles Consecutive Angles

• Corresponding Angles Two angles that occupy
  corresponding positions.

? 2 ? ? 6, ? 1 ? ? 5, ? 3 ? ? 7, ? 4 ? ? 8
1
2
3
4
5
6
7
8
6
Consecutive Angles

• Consecutive Interior Angles Two angles that lie
  between parallel lines on the same sides of the
  transversal.
• Consecutive Exterior Angles Two angles that lie
  outside parallel lines on the same sides of the
  transversal.

m?3 m?5 180º, m?4 m?6 180º
1
2
m?1 m?7 180º, m?2 m?8 180º
3
4
5
6
7
8
7
Alternate Angles

• Alternate Interior Angles Two angles that lie
  between parallel lines on opposite sides of the
  transversal (but not a linear pair).
• Alternate Exterior Angles Two angles that lie
  outside parallel lines on opposite sides of the
  transversal.

? 3 ? ? 6, ? 4 ? ? 5
? 2 ? ? 7, ? 1 ? ? 8
1
2
3
4
5
6
7
8
8
Example If line AB is parallel to line CD and s
is parallel to t, find the measure of all the
angles when mlt 1 100. Justify your answers.
mlt280 mlt3100 mlt480
mlt5100 mlt680 mlt7100 mlt880
mlt9100 mlt1080 mlt11100 mlt1280
mlt13100 mlt1480 mlt15100 mlt1680
9
Example
If line AB is parallel to line CD and s is
parallel to t, find
1. the value of x, if mlt3 4x 6 and the mlt11
126.
2. the value of x, if mlt1 100 and mlt8 2x
10.
3. the value of y, if mlt11 3y 5 and mlt16
2y 20.
ANSWERS
1. 30
2. 35
3. 33