Parallel Lines and Transversals

Parallel Lines and Transversals

Parallel Lines and Transversals What would you call two lines which do not intersect? Parallel B  A

D C

 A solid arrow placed placed on two lines of a diagram indicate the lines are parallel. The symol !! is used to indicate parallel lines.  AB !! CD

Parallel Lines and Transversals  A slash through the parallel symol !! indicates the lines are not parallel.

B

 AB !! CD

 A D C

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 .

 A C

B D

"ince the lines are not in the same plane% they are skew lines.

Parallel Lines and Transversals &or the rectangular o' shown elow% find (. All planes parallel to plane CD).

Parallel Lines and Transversals &or the rectangular o' shown elow% find )

*

&

, C

D

 A

(. All planes parallel to plane CD).

B

Plane BA* +or any plane with BA*,-.

Parallel Lines and Transversals &or the rectangular o' shown elow% find . The intersection of plane A*) and plane C&).

Parallel Lines and Transversals &or the rectangular o' shown elow% find ) *

& ,

. The intersection of plane A*) and plane C&).

C

D

 ED  A

B

Parallel Lines and Transversals &or the rectangular o' shown elow% find /. All segments parallel to CD.

Parallel Lines and Transversals &or the rectangular o' shown elow% find /. All segments parallel to CD.  AB% ,*% )&

Parallel Lines and Transversals &or the rectangular o' shown elow% find 0. All segments that intersect C&.

Parallel Lines and Transversals &or the rectangular o' shown elow% find 0. All segments that intersect C&.

 BC ,

AC ,

GF ,

EF  

DC 

Parallel Lines and Transversals &or the rectangular o' shown elow% find 1. All lines s#ew to ,&.

Parallel Lines and Transversals &or the rectangular o' shown elow% find 1. All lines s#ew to ,&.  AB,

AC ,

 AH ,

DE 

AB

"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 ,&.

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.

 3

#

m t

Lines 3% #% and m are intersected y line t. Therefore% line t is a transversal of lines  3% #% and m.

Parallel Lines and Transversals 4dentifying Angles 2

 3 ( /  0

# 1 6 5 7

t

)'terior angles are on the exterior  of the two lines cut y the transversal. The e'terior angles are8 ∠1,

∠2,

∠7,

∠8

Parallel Lines and Transversals 4dentifying Angles 2

 3 ( /  0

# 1 6 5 7

t

4nterior angles are on the interior  of the two lines cut y the transversal. The interior angles are8 ∠3,

∠4,

∠5,

∠6

Parallel Lines and Transversals 4dentifying Angles 2

 3 ( /  0

# 1 6 5 7

t

Consecutive interior angles are on the interior  of the two lines and on the same side of the transversal. Consecutive interior angles are8 ∠3

and 

∠5,

or  ∠4

and 

∠6

Parallel Lines and Transversals 4dentifying Angles 2

 3 ( /  0

# 1 6 5 7

t

 Alternate interior angles are on the interior  of the two lines and on opposite sides of the transversal.  Alternate interior angles are8 ∠3

and 

∠6,

or  ∠4

and 

∠5

Parallel Lines and Transversals 4dentifying Angles 2

 3 ( /  0

# 1 6 5 7

t

 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

and 

∠8,

or  ∠2

and 

∠7

Parallel Lines and Transversals 4dentifying Angles 2

 3 ( /  0

# 1 6 5 7

t

Consecutive interior angles are on the interior  of the two lines and on the same side of the transversal. Consecutive interior angles are8 ∠3

and 

∠5,

or  ∠4

and 

∠6

Parallel Lines and Transversals 4dentifying Angles 2

 3 ( /  0

# 1 6 5 7

t

Corresponding angles are on the corresponding side of the two lines and on the same side of the transversal. Corresponding angles are8 ∠1 and  ∠5, ∠3

and 

∠7,

∠2

and

∠6, or  

∠4

and 

∠8

Parallel Lines and Transversals 4dentifying Angles $ Chec# for :nderstanding 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 0 / oth lines in a plane.  ( 5 1 7 6 . ∠  and ∠(9 are alternate interior angles. ; (9 &alse 2 The angles are (( ( corresponding angles on (5 (1 (0 (/ transversal p.

Parallel Lines and Transversals 4dentifying Angles $ Chec# for :nderstanding Determine if the statement is true or false. 4f false% correct the statement. /. ∠/ and ∠ 1 are alternate interior angles.

(

 7 6 ; (9

/

0

5 1

(( (

(5 (1 (0 (/

&alse $ The angles are vertical angles created y the intersection of q and r . 0. ∠( and ∠(1 are alternate e'terior angles. True 2 The angles are alternate e'terior angles on transversal p.

Parallel Lines and Transversals 4dentifying Angles $ Chec# for :nderstanding Determine if the statement is true or false. 4f false% correct the statement. 1. ∠5 and ∠ ( are alternate interior angles.

(

 7 6 ; (9

/

0

5 1

(( (

(5 (1 (0 (/

True $ The angles are alternate interior angles on transversal q. 5. ∠(9 and ∠(( are consecutive interior angles. True $ The angles are consecutive interior angles on transversal s.

Parallel Lines and Transversals 4dentifying Angles $ Chec# for :nderstanding Determine if the statement is true or false. 4f false% correct the statement. 6. ∠/ and ∠ 0 are alternate e'terior angles.

(

 7 6 ; (9

/

0

5 1

(( (

(5 (1 (0 (/

&alse $ The angles are a linear pair with linear rays on line r . 7. ∠(5 and ∠(0 are corresponding angles. True $ The angles are corresponding on transversal s.