Title: Angles%20and%20Parallel%20Lines
1Lesson 2-4
- Angles and Parallel Lines
2Transversal
- 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
3Vertical 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
4Angles 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..
5Corresponding 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
6Consecutive 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
7Alternate 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
8Example 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
9Example
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