PLANE G

EOMETRY

UNIT 1

– CHAPT

ER 1

SE

CT

I ON

1. 1

– I DE

NT

I FY

PO

I NT

S, L

I NE

S, A

ND

PL

AN

ES

DA

Y 1

SECTION 1.1 NOTES

Undefined Terms – Vocabulary without a formal definition, but overall agreement with what the term means.

Point – representation of a unique location in space. It has no dimension.

Line – connection of an infinite number of points. It has one dimension.

P

A B Cl

LINE NOTATION:Line l, Line AB ( AB ), Line ( BC ), or Line AC ( AC )

SECTION 1.1 NOTES

Compare and Contrast:

Line – Infinite in length, extends endlessly in opposite directions.

Segment – Finite portion of a line that begins and ends at endpoints (points on that line).

Ray – Infinitely long portion of a line that begins at an initial point and extends endlessly in one direction.

A B

A

AB

B

A B

AB

ABRAY NOTATION:

Point with no arrow head is called endpoint, always list endpoint first and always draw arrow pointing right.

Endpoint

SECTION 1.1 NOTES

Extension:

Opposite Rays – two rays that share the same endpoint but extend in exactly opposite directions. They =alwys form a straight line.

What are the opposite rays for the image given?

A IH

HA

Endpoint

HI

SECTION 1.1 NOTES

Plane – a flat surface that contains an infinite amount of lines and extends endlessly in two directions.

W

OC

M

PLANE NOTATION:Use any three points that lie on the plane and that do not lie in a line, or if a letter already represents it.

PLANE NOTATION:Plane M, or Plane COW, Plane WOC, Plane OCW

SECTION 1.1 NOTES

Collinear Points – points that all lie on the same line.

Coplanar Points – points that all lie on the same plane.

A B C D

G

OS

H

SECTION 1.1 NOTES

Identification, name:

The plane:

HOD, DOG, DGH

A Line:

AB, OB, HG, GO, …

A Segment:

GO, AO, BO, HG, …

A Ray:

OG, GH, BA, AB, HG, …

A

B

D

G

O

H

SECTION 1.1 NOTES

Identification, Collinear or not?

A) B, D

B) C, E

C) A, D

D) B, F

E) F, E, D

F) A, E, D

G) D, B, C

H) C, E, F

E

F

A

B

C

D

YES

YES

YES

YES

NO

NO

YES

YES

SECTION 1.1 NOTES

Identification, Coplanar or not?

A) B, C, D

B) A, B, C

C) F, E, D

D) E, A, F

E) A, B, C, D

F) F, E, D, C

G) E, A, D, C

H) B, C, D, E, F

E

F

A

B

C

D

YES

YES

YES

YES

YES

YES

NO

YES

SECTION 1.1 NOTES

Intersections: 2 lines always intersect at a point (Figure 1) A line that does not lie on a plane can intersect a

plane at a point. (Figure 2)

W

O

CE

F

CM

P

Figure 1

Figure 2

Intersection Intersecti

on

SECTION 1.1 NOTES

Intersections: (cont.) 2 Planes always

intersect at a line (Figure 3)

Figure 3

M

Q

a

Intersection: Line a

CHECK FOR UNDERSTANDING…TIME TO DRAW…Four coplanar points…three or which are

collinear.

A

B

C

D

CHECK FOR UNDERSTANDING…TIME TO DRAW…Two coplanar lines that do NOT intersect.

B C D

F E H

CHECK FOR UNDERSTANDING…TIME TO DRAW…Opposite rays AB and AC.

B CA

AB

Endpoint

AC

CHECK FOR UNDERSTANDING…TIME TO DRAW…Three planes that do not intersect.

M

A

B

CHECK FOR UNDERSTANDING…TIME TO DRAW…Three coplanar lines that intersect at the

same point.

B

CD

F

E

H

E

B

CHECK FOR UNDERSTANDING…TIME TO DRAW…Two planes that intersect one another.

M

Q

a

CHECK FOR UNDERSTANDING…TIME TO DRAW…Two lines that intersect and a third line that

does not intersect either of them.E

F

A

B

C

D

H

G

CHECK FOR UNDERSTANDING…TIME TO DRAW…Three lines that intersect at a point but are

not coplanar. A

B

D

G

O H

F

CONCEPT CHECK

P. 3-5

#1 – 7

“Guided Practice”

HOMEWORKP. 5-6

#3 - 26

(Omit #12)