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Aim: What are Transversals and Angle Pairs? Parallel Lines?

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Aim: What are Transversals and Angle Pairs? Parallel Lines?

Do Now:

Below are 2 intersecting straight lines. Describe 2 different methods of finding the value of x.

1. Intersecting lines form vertical angles that are opposite each other and congruent. Therefore you can find the value of x by putting 10x - 18 = 8x + 10 or 7x - 40 = 5x - 12 and solving for x.

10x - 18

7x - 40

5x - 12

8x + 10

Do Now:

2. There are 4 linear pair in this diagram: angles that are adjacent and supplementary. Therefore you can find the value of x by solving any of four equations:

10x - 18

7x - 40

5x - 12

8x + 10

10x - 18 + 5x - 12 = 180

5x - 12 + 8x + 10 = 180

8x + 10 + 7x - 40 = 180

7x - 40 + 10x - 18 = 180

x = 14

m

m is a transversal

l

p

Transversals

A line that intersects more than one line is called a transversal.

Exterior zone

Interior zone

Exterior zone

Zones formed by

Transversals

m

l

p

Alternate Sides formed by

Transversals

m

Exterior zone

l

Interior zone

p

Exterior zone

The Importance of Parallel

Parallel Lines

Parallel Lines

A

B

l

AB | | CD

or

l| |p

p

C

D

Two or more lines are parallel if and only if the lines lie in the same plane but do not intersect.

| | means “is parallel to”

Angles formed by

Transversals

l | | p

m

1

2

l

3

4

5

6

7

8

p

2 and 3 are congruent vertical angles

6 and 7 are congruent vertical angles

If l | | p then 2 3 6 7

Angles formedby

Transversals

m

l | | p

1

2

l

3

4

5

6

7

8

p

1 and 4 are congruent vertical angles

5 and 8 are congruent vertical angles

Since l | | p then 1 4 5 8

1

2

7

8

Alternate Exterior Angles

m

l

3

4

5

6

p

1 and 8 are alternate exterior angles

If l | | p then 1 8

2 and 7 are alternate exterior angles

If l | | p then 2 7

A

If two parallel lines are cut by a transversal, then the Alternate ExteriorAngles formed are congruent.

3

4

5

6

Alternate InteriorAngles

m

1

2

l

7

8

p

3 and 6 are alternate interior angles

If l | | p then 3 6

4 and 5 are alternate interior angles

If l | | p then 4 5

A

If two parallel lines are cut by a transversal, then the Alternate InteriorAngles formed are congruent.

3

4

5

6

InteriorAngles on Same Side

m

1

2

l

7

8

p

3 and 5 are interior angles

If l | | p then 3 & 5 are supplementary

3 and 6 are interior angles

If l | | p then 3 & 5 are supplementary

If two parallel lines are cut by a transversal, then the InteriorAngles on the same side of the transversal are supplementary.

1 and 5

2 and 6

If l | | p then

3 and 7

4 and 6

Corresponding Angles

m

1

2

l

3

4

5

6

7

8

p

Corresponding Angles

1 5

2 6

3 7

4 6

A

If two parallel lines are cut by a transversal, then the Corresponding Angles formed are congruent.

l is parallel to m

Name the alternate exterior angles

Name the corresponding angles

Name the interior angles

Name the exterior angles

Name the alternate interior angles

m

l

w

x

z

y

p

q

s

r

p

Find the measure of each angle if 1 = 1370.

m

1370

430

l

1

2

4

3

430

1370

1370

430

6

5

7

8

p

430

1370

Note: 1 and 2 are a linear pair. How many other linear pairs are there in this diagram?

7 other linear pairs - 2 & 4; 4 & 3; 3 & 1; 5 & 6; 6 & 8; 8 & 7; and 7 & 5.

AB | | CD Find the measure of each angle if AHF = 8x - 20 and CGH = 4x + 44.

F

720

1080

A

B

720

H

1080

1080

720

G

D

720

C

1080

AHF and CGH are Corresponding Angles and therefore are congruent

E

8(16) - 20 = 1080

8x - 20 = 4x + 44

1800 - 1080 = 720

4x - 20 = 44

4x = 64

x = 16

The measure of b is twice the measure of a. What is the measure of each angle.

AB | | CD

A

B

a

b

D

C

F

The measure of a is five times the measure of b. What is the measure of y.

AB | | CD

y

A

B

a

b

D

C

F

Give two ways to find the measure of y.

AB | | CD

150o

x

z

A

B

y

D

C

F

Find the measure of all angles.

AB | | CD | | EF

o

75o

A

p

q

B

r

s

C

u

v

D

w

x

E

y

z

F

G

E

D

B

C

A

F

Skew Lines

Lines in space that never meet and are not in the same plane are skew lines.