Parallel Lines and Transversals

(1)

Parallel Lines and

Transversals

(2)

A A B B D D C C

Parallel Lines and Transversals

What would you call two lines which do not intersect? What would you call two lines which do not intersect?

Parallel

A

A solid arrow plsolid arrow placedaced on two lines of a

on two lines of a

diagram indicate the diagram indicate the lines are parallel.

lines are parallel. The

The symol symol !! !! is is used used toto indicate parallel lines.

indicate parallel lines. AB

(3)

Parallel Lines and Transversals

A slash through the parallel symol !! indicates the lines are not parallel.

AB !! CD

A

D

B

(4)

Parallel Lines and Transversals

"#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 not in the same plane%

they are skew lines.

A

B

C

(5)

Parallel Lines and Transversals

&or the rectangular o' shown elow% find

(. All planes parallel to plane CD).

(6)

Parallel Lines and Transversals

(. All planes parallel to plane CD).

Plane BA* +or any plane with BA*,-. A * ) , & B C D

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Parallel Lines and Transversals

. The intersection of plane A*) and

(8)

Parallel Lines and Transversals

. The intersection of plane A*) and

plane C&).

ED

A * ) , & B C D

(9)

Parallel Lines and Transversals

/. All segments parallel to CD.

(10)

AB% ,*% )&

Parallel Lines and Transversals

/. All segments parallel to CD.

(11)

Parallel Lines and Transversals

0. All segments that intersect C&.

(12)

Parallel Lines and Transversals

0. All segments that intersect C&.

,

BC AC DC GF EF

(13)

Parallel Lines and Transversals

1. All lines s#ew to ,&.

(14)

Parallel Lines and Transversals

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

(15)

Parallel Lines and Transversals

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

# 3

Lines 3% #% and m are intersected y line t.

Therefore% line t is a

transversal of lines 3% #% and m.

(16)

Parallel Lines and Transversals

4dentifying Angles 2

t

#

3

(  / 0 1 5 6 7

)'terior angles are on the exterior of the

two lines cut y the transversal.

The e'terior angles are8

1,

2,

7,

8

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Parallel Lines and Transversals

t

#

3

(  / 0 1 5 6 7

4nterior angles are on the interior of the two lines cut y the

transversal.

The interior angles are8

3,

4,

5,

6

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Parallel Lines and Transversals

t

#

3

(  / 0 1 5 6 7 Consecutive interior

angles are on the interior

of the two lines and on the

same side of the transversal.

Consecutive interior angles are8

3 5,

4

6

and or and ∠ ∠ ∠ ∠

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Parallel Lines and Transversals

t

#

3

(  / 0 1 5 6 7

Alternate interior angles are on the interior of the two lines and on opposite sides of the transversal.

Alternate interior angles are8

3 6,

4

5

(20)

Parallel Lines and Transversals

t

#

3

(  / 0 1 5 6 7

Alternate e'terior angles are on the exterior of the two lines and on opposite sides of the transversal.

Alternate e'terior angles are8

1 8,

2

7

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Parallel Lines and Transversals

t

#

3

(  / 0 1 5 6 7 Consecutive interior

angles are on the interior

of the two lines and on the

same side of the transversal.

Consecutive interior angles are8

3 5,

4

6

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Parallel Lines and Transversals

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.

Parallel Lines and Transversals

∠

4dentifying Angles $ Chec# for :nderstanding

(  / 0 1 5 6 7 ; (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.

(24)

0. ( and (1 are

alternate e'terior angles. /. / and 1 are

Parallel Lines and Transversals

∠

(  / 0 1 5 6 7 ; (9 _{(( (} (/ (0 (1 (5

&alse $ The angles are vertical angles created y the intersection of q

and r . ∠

True 2 The angles are alternate e'terior angles on transversal p.

(25)

5. (9 and (( are

consecutive interior angles. 1. 5 and ( are

Parallel Lines and Transversals

∠

(  / 0 1 5 6 7 ; (9 _{(( (} (/ (0 (1 (5

True $ The angles are alternate interior angles on transversal q.

∠

True $ The angles are consecutive interior

angles on transversal s.

(26)

Determine if the statement is true or false. 4f false% correct the statement. 6. / and 0 are

alternate e'terior angles.

7. (5 and (0 are corresponding angles.

Parallel Lines and Transversals

∠

(  / 0 1 5 6 7 ; (9 _{(( (} (/ (0 (1 (5

&alse $ The angles are a linear pair with linear rays on line r .

∠

True $ The angles are corresponding on

transversal s.