1 / 9

# Lesson 2-4 - PowerPoint PPT Presentation

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

Related searches for Lesson 2-4

I am the owner, or an agent authorized to act on behalf of the owner, of the copyrighted work described.

Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author.While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server.

- - - - - - - - - - - - - - - - - - - - - - - - - - E N D - - - - - - - - - - - - - - - - - - - - - - - - - -
Presentation Transcript
Lesson 2-4

Lesson 2-4: Angles and Parallel Lines

• 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

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

• 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: 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 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

Lesson 2-4: Angles and Parallel Lines

• 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.