Lesson 2-4

- Angles and Parallel Lines

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

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

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..

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

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

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

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

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