Cover Slide

Identifying Points, Lines

And Planes

3 Undefined Terms

Points, Lines, and Planes

The 3 Undefined Terms of Geometry

Points, Lines, and Planes

• undefined geometric terms

• described instead of defined• a starting “point” for us to build on• used in the definitions of more complex geometric figures

• three most basic figures in geometry

Points

Points, Lines, and Planes

Points

Examples: a dot or a star

Named: usually by a capital letter

A

B

C Points A, B and C

• no actual size• sometimes represented by objects that do have size• all geometric figures are composed of points

Lines

Points, Lines, and Planes

Named: usually by a lower-case letter (sometimes script)by any two points on the line and the line symbol

Example: the dotted lines on a street or highway

or

b

bE

Dline DEline ED

DEED

• series of points extending indefinitely in two directions• no thickness or width• represented by a figure that does have thickness

Ways to namethe line to the left:

Lines

Planes

Points, Lines, and Planes

Example: a ceiling or a wall

Named: usually by a capital letter (sometimes script)by any three points that are not on the same line but are in that plane

or

K

plane RST

Planes• a flat surface• no thickness or width• extends indefinitely in all directions

Ways to name the plane to the right:

KR S

T

Collinear/Noncollinear

Definitions

Collinear• points that lie on the same line

Noncollinear• points that do not lie on the same line

CB

DB, C, and D are collinear

E

FGE, F, and G are noncollinear

One line could not pass through all 3 points.

Coplanar/Noncoplanar

Definitions

Coplanar• points that lie in the same plane

Noncoplanar

• points that do not lie in the same plane

CB D

A, B, C, and D are coplanar

E F

GE, F, G, and H are noncoplanar

A

H

Space/Intersection

Definitions

Space

Intersection• the intersection of two figures is the set of points that are in both figures

• the set of all points• three-dimensional • points, lines, and planes are contained in space

Some examples of intersection will be demonstrated on the following slides.

Relation line-point, 2 lines

Point, Line, and Plane - Relationships

S

R

d

a b

S is on d. S is in d.

d passes through S.d contains S.

The intersection of d and S is S.

The intersection of a and b is R.

a and b intersect at R.

a and b intersect in R.

both a and b contain R.

Relation line-plane, 2 planes

Point, Line, and Plane - Relationships

b and D are in W. W contains b and D.

The intersection of a and W is D.

C

B

X

Y

a intersects W at D. D

W

b

a

a and b do not intersect.

BC is in Y and X. Y and X both contain BC.

Y and X intersect in BC.

All points on BC are in Y and X.The intersection of Y and X is BC.

Q & A prob. 1-6 (T or F)

Q & A

A

B

C

D

E

H

F

NJ

KL

M

Determine whether each statement is

true or false.

1.

2.

3.

4.

5.

6.

A, M, and C are collinear.

F, L, B, and C are coplanar.

D, M, and B are coplanar.

A, C, and E are collinear.

E, L, K, and B are coplanar.

A, C, and E are coplanar.

true

true

false

false

true

true

Q & A prob. 1-5

Q & A

A

B

C

D

E

H

F

NJ

KL

M

Refer to the figure at the left to answer each question.

B

planes BDH & EDH

C, K

planes FAD, FED, BND

C

1.

2.

3.

4.

5.

Name 3 planes thatintersect at D.

Name all points coplanarwith E, H, and B.

Name the intersection ofBC and NB.

Name two planes thatintersect in DH.

Name the intersectionof BC and plane EFA.