course: applied geometry aim: parallel lines aim: what are transversals and angle pairs? parallel...

Course: Applied GeometryAim: Parallel Lines

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.

10x - 18

5x - 127x - 40

8x + 10

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

5x - 127x - 40

8x + 10

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 + 5x - 12 = 180

5x - 12 + 8x + 10 = 180

8x + 10 + 7x - 40 = 180

7x - 40 + 10x - 18 = 180

x = 14

Do Now:


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

l

pm is

a

transvers

al

m


Exterior zone

Zones formed by

l

m

Interior zone

Exterior zone p


Alternate Sides formed by

l

p

mExterior zone

Exterior zone

Interior zone


The Importance of Parallel


Angles formed by

l

p

m

41

58

23

67

2 and 3 are congruent vertical angles


l | | p

If l | | p then 2 3 6 7


Angles formed by

l

p

m

243

1

5 67 8



Since l | | p then 1 4 5 8

l | | p


l

p

m

1

8

2

7

1 and 8 are alternate exterior angles

2 and 7 are alternate exterior angles

If l | | p then 1 8

If l | | p then 2 7

A

Alternate Exterior AnglesAlternate Exterior Angles

If two parallel lines are cut by a transversal, then the Alternate ExteriorAlternate Exterior AnglesAngles formed are

congruent.

43

5 6


l

p

m

21

7 8

4

5

3

6

3 and 6 are alternate interior angles

4 and 5 are alternate interior angles

If l | | p then 3 6

If l | | p then 4 5

A

Alternate InteriorAlternate Interior AnglesAngles

If two parallel lines are cut by a transversal, then the Alternate InteriorAlternate Interior AnglesAngles formed are

congruent.


l

p

m

21

7 8

3

5

4

6

3 and 5 are interior angles

3 and 6 are interior angles

If l | | p then 3 & 5 are supplementary

If l | | p then 3 & 5 are supplementary

InteriorInterior Angles on Same SideAngles on Same Side

If two parallel lines are cut by a transversal, then the InteriorInterior Angles Angles on the same side of the

transversal are supplementary.


l

p

m

243

1

5 67 8

Corresponding Angles

A

Corresponding AnglesCorresponding Angles

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

3 and 72 and 61 and 5

4 and 63 72 61 5

4 6

If l | | p then


l

p

m

l is parallel to m

w xyz

qprs

Name the exterior anglesName the interior anglesName the corresponding anglesName the alternate interior anglesName the alternate exterior angles


l

p

mFind the measure of each angle if 1 = 1370.

13 4

5 67 8

430

1370

1370

430

1370 430

1370

2

430

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.

1080

E

GC D

H B

F

AHF and CGH are Corresponding Angles and therefore are congruent

8x - 20 = 4x + 44

4x - 20 = 44

4x = 64

x = 16

8(16) - 20 = 1080

1080

1080

1080

A

1800 - 1080 = 720

720

720

720

720


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

C D

B

F

A

b

a

AB | | CD


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

C D

B

F

A

ba

AB | | CDy


Give two ways to find the measure of y.

C D

B

F

A zx

AB | | CD150o

y


Find the measure of all angles.

C

D

B

G

Aqp

AB | | CD | | EF75o

E

F

o

sr

vu

xw

zy


Skew Lines

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

A

B C

DE

F

course: applied geometry aim: parallel lines aim: what are transversals and angle pairs? parallel...

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