ch 3-1 parallel lines and transversals

8/17/2019 Ch 3-1 Parallel Lines and Transversals

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Parallel Lines and

Transversals


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AB

D

C

Parallel Lines and Transversals

What would you call two lines which do not intersect?

Parallel

A solid arrow placedon two lines of a

diagram indicate the

lines are parallel.

The symol !! is used to

indicate parallel lines.

AB !! CD


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A slash through the parallel symol !! indicates the

lines are not parallel.

AB

!! CD

A D

B

C


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"#ew Lines $

Two lines are s#ew if they are not in the

same plane and do not intersect.

AB does not intersect

CD .

"ince the lines are notin the same plane%

they are skew lines.

A

BC

D


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&or the rectangular o' shown elow% find

(. All planes parallel

to plane CD).


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(. All planes parallel

to plane CD).

Plane BA* +or

any plane with

BA*,-. A

*

)

,

&

B

CD


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. The intersection of

plane A*) andplane C&).


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. The intersection of

plane A*) andplane C&).

ED A

*

)

,

&

B

CD


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/. All segments

parallel to CD.


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AB% ,*% )&



/. All segments

parallel to CD.


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0. All segments that

intersect C&.


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0. All segments that

intersect C&.

, ,

,

BC AC DC

GF EF


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1. All lines s#ew to

,&.


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1. All lines s#ew to

,&.

, ,,

AB AC AB

AH DE

"egments *)% AD% and BC are

!! or in the same plane.

"egments ,*% )&% B, and C&

intersect and are in the same

plane. These segments are

not s#ew to ,&.


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Transversal 2

A transversal is a line which intersects two or

more lines in a plane. The intersected lines do

not have to e parallel.

t

m# 3Lines 3% #% and m are

intersected y line t.

Therefore% line t is a

transversal of lines 3% #% and m.


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4dentifying Angles 2

t

# 3

(

/

0

1

5

6

7

)'terior angles are on

the exterior of the

two lines cut y thetransversal.

The e'terior angles are8

1, 2, 7, 8∠ ∠ ∠ ∠


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t

# 3

(

/

0

1

5

6

7

4nterior angles are on

the interior of the two

lines cut y thetransversal.

The interior angles are8

3, 4, 5, 6∠ ∠ ∠ ∠


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t

# 3

(

/

0

1

5

6

7

Consecutive interior

angles are on the interior

of the two lines and on thesame side of the

transversal.

Consecutive interior angles are8

3 5,

4 6

and

or

and

∠ ∠

∠ ∠


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t

# 3

(

/

0

1

5

6

7

Alternate interior angles

are on the interior of

the two lines and onopposite sides of the

transversal.

Alternate interior angles are8

3 6,

4 5

and

or

and

∠ ∠

∠ ∠


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t

# 3

(

/

0

1

5

6

7

Alternate e'terior angles

are on the exterior of

the two lines and onopposite sides of the

transversal.

Alternate e'terior angles are8

1 8,

2 7

and

or

and

∠ ∠

∠ ∠


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t

# 3

(

/

0

1

5

6

7

Consecutive interior

angles are on the interior

of the two lines and on thesame side of the

transversal.

Consecutive interior angles are8

3 5,

4 6

and

or

and

∠ ∠

∠ ∠


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t

# 3

(

/

0

1

5

6

7

Corresponding angles are

on the corresponding

side of the two lines and

on the same side of the

transversal.

Corresponding angles are8

1 5,

3 7,

2 6,

4 8

and

and

and or

and

∠ ∠

∠ ∠

∠ ∠

∠ ∠


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. and (9 are

alternate interior angles.


∠

4dentifying Angles $ Chec# for :nderstanding

( / 0

1567

; (9 (( (

(/(0(1(5

Determine if the statement is true or false. 4f false%

correct the statement.(. Line r is a transversal

of lines p and q.

True $ Line r intersects

oth lines in a plane.

∠

&alse 2 The angles are

corresponding angles on

transversal p.


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0. ( and (1 arealternate e'terior angles.

/. / and 1 are



∠

∠


( / 0

1567

; (9 (( (

(/(0(1(5


correct the statement.

&alse $ The angles arevertical angles created

y the intersection of q

and r .

∠

True 2 The angles are

alternate e'terior angles

on transversal p.

∠


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5. (9 and (( areconsecutive interior angles.

1. 5 and ( are



∠

∠


( / 0

1567

; (9 (( (

(/(0(1(5


correct the statement.

True $ The angles arealternate interior angles

on transversal q.

∠

True $ The angles are

consecutive interior

angles on transversal s.

∠


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correct the statement. 6. / and 0 are

alternate e'terior angles.

7. (5 and (0 arecorresponding angles.


∠

∠


( / 0

1567

; (9 (( (

(/(0(1(5

&alse $ The angles area linear pair with linear

rays on line r .

∠

True $ The angles are

corresponding on

transversal s

∠

ch 3-1 parallel lines and transversals

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