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Angles and Parallel Lines. Lesson 2-4. 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

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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

Lesson 2-4: Angles and Parallel Lines

Vertical Angles & Linear Pair

Two angles that are opposite angles. Vertical angles are congruent.

Vertical Angles:

Linear Pair:

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

Lesson 2-4: Angles and Parallel Lines

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…..

Lesson 2-4: Angles and Parallel Lines

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

Lesson 2-4: Angles and Parallel Lines

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.

m3 +m5 = 180º, m4 +m6 = 180º

1

2

m1 +m7 = 180º, m2 +m8 = 180º

3

4

5

6

7

8

Lesson 2-4: Angles and Parallel Lines

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

Lesson 2-4: Angles and Parallel Lines

A

1

2

10

9

12

11

4

3

C

D

5

6

13

14

15

16

7

8

s

t

Example:If line AB is parallel to line CD and s is parallel to t, find the measure of all the angles when m< 1 = 100°. Justify your answers.

m<2=80° m<3=100° m<4=80°

m<5=100° m<6=80° m<7=100° m<8=80°

m<9=100° m<10=80° m<11=100° m<12=80°

m<13=100° m<14=80° m<15=100° m<16=80°

Lesson 2-4: Angles and Parallel Lines

A

1

2

10

9

12

11

4

3

C

D

5

6

13

14

15

16

7

8

s

t

Example:If line AB is parallel to line CD and s is parallel to t, find:

1. the value of x, if m<3 = 4x + 6 and the m<11 = 126.

2. the value of x, if m<1 = 100 and m<8 = 2x + 10.

3. the value of y, if m<11 = 3y – 5 and m<16 = 2y + 20.

ANSWERS:

1. 30

2. 35

3. 33

Lesson 2-4: Angles and Parallel Lines

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