1 4 segments, rays, parallel lines and planes

Sec. 1 – 4 Sec. 1 – 4 Segments, Rays, Parallel Segments, Rays, Parallel

Lines and PlanesLines and Planes

Objectives:Objectives:

1) Identify segments and rays.1) Identify segments and rays.

2) Recognize parallel lines.2) Recognize parallel lines.

LineLine – A series of points that extend in 2 – A series of points that extend in 2 directions without end.directions without end.– Notation: 2 capital letters with a line over Notation: 2 capital letters with a line over

them.them.

– Ex:Ex:– Reads: Line AB Reads: Line AB

A B

AB

SegmentSegment – Is the part of a line consisting – Is the part of a line consisting of two endpoints & all the points between of two endpoints & all the points between them.them.– Notation: 2 capital letters with a line over Notation: 2 capital letters with a line over

them.them.

– Ex:Ex:– No arrows on the end of a line. No arrows on the end of a line. – Reads: Line segment (or segment) AB Reads: Line segment (or segment) AB

A B

ABAB refers to the segment

AB refers to the length of AB

Ray Ray – Is the part of a line consisting of one – Is the part of a line consisting of one endpoint & all the points of the line on one endpoint & all the points of the line on one side of the endpoint.side of the endpoint.– Notation: 2 capital letters with a line with an Notation: 2 capital letters with a line with an

arrow on one end of it. End point always arrow on one end of it. End point always comes first.comes first.

– Ex: Ex: – Reads: Ray ABReads: Ray AB

A B

AB

Opposite RaysOpposite Rays – Are two – Are two collinearcollinear rays rays with the same endpoint. with the same endpoint. – Opposite rays always form a line.Opposite rays always form a line.

– Ex: Ex:

Same Line

Q R S

RQ & RS

Endpoints

Ex.1: Naming segments and rays.Ex.1: Naming segments and rays.

Name 3 segments:Name 3 segments:– LPLP– PQPQ– LQLQ

Name 4 rays:Name 4 rays:– LQLQ– QLQL– PLPL– LPLP– PQPQ

L P Q

Are LP and PL opposite rays??

No, not the same endpoints

Are LP and LQ different rays??

No, they the same same ray.

Parallel LinesParallel Lines – Are coplanar lines that – Are coplanar lines that never intersect.never intersect.– Coplanar – same planeCoplanar – same plane– Symbol Symbol [ // ][ // ]– Ex: r // tEx: r // t– Reads: line r is parallel to line t.Reads: line r is parallel to line t.

rt

Skew LinesSkew Lines – Are noncoplanar lines that – Are noncoplanar lines that never intersect.never intersect.– Skew lines are never //Skew lines are never //

Parallel PlanesParallel Planes – Are planes that do not – Are planes that do not intersect.intersect.

A

B

C

D

E

F

G

H

A

B

DC

What would you call two lines which do not intersect?

Parallel

A solid arrow placed on two lines of a diagram indicate the lines are parallel.

The symbol || is used to indicate parallel lines.

AB || CD

A slash through the parallel symbol || indicates the lines are not parallel.

AB || CD

AD

B

C

Skew Lines –

Two lines are skew if they are not in the same plane and do not intersect.

AB does not intersect CD .

Since the lines are not in the same plane, they are skew lines.

A

BC

D

For the rectangular box shown below, find

1. All planes parallel to plane CDE.

For the rectangular box shown below, find

1. All planes parallel to plane CDE.

Plane BAH (or any plane with BAHG).

A

H

E

G

F

B

CD

Parallel Lines and Transversals

For the rectangular box shown below, find

2. The intersection of plane AHE and plane CFE.

For the rectangular box shown below, find

2. The intersection of plane AHE and plane CFE.

EDA

H

E

G

F

B

CD

For the rectangular box shown below, find

3. All segments parallel to CD.

AB, GH, EF

Parallel Lines and Transversals

For the rectangular box shown below, find

3. All segments parallel to CD.

For the rectangular box shown below, find

4. All segments that intersect CF.

For the rectangular box shown below, find

4. All segments that intersect CF.

, ,

,

BC AC DC

GF EF

For the rectangular box shown below, find

5. All lines skew to GF.

For the rectangular box shown below, find

5. All lines skew to GF.

, ,

,

AB AC AB

AH DE

Segments HE, AD, and BC are || or in the same plane. Segments GH, EF, BG and CF intersect and are in the same plane. These segments are not skew to GF.

Use the figure below. Name all segments that

are parallel to AE. Name all segments that are skew to AE.

Parallel segments lie in the same plane, and the lines that contain them do not intersect. The three segments in the figure above that are parallel to AE are BF, CG, and DH.

1-3

Skew lines are lines that do not lie in the same plane. The four lines in the figure that do not lie in the same plane as AE are BC, CD, FG, and GH.

Parallel to GJ?Skew to GJ?

HI, DNAB, CD, CH

What have we learned??What have we learned??

Name the following line.Name the following line.

Name a segment.Name a segment.

Name a ray.Name a ray.

X

Y

ZXY or YZ or ZX

XY or YZ or XZ

XY or YZ or ZX or YX

Parallel LinesParallel Lines ~ ~ coplanar lines that do coplanar lines that do not intersectnot intersect

Skew LinesSkew Lines ~ ~ noncoplanar noncoplanar They are not parallel They are not parallel & they do not intersect& they do not intersect

Same direction &Same plane

Different direction &Different

plane

Lines that do not intersect Lines that do not intersect

may or may not be may or may not be coplanar.coplanar.

Homework- Pg. 25 # 3 – 23 , 25-33 write out sentences, 34, 44, 46 - 49

Don’t forget 25-33, write out sentences