Coplanar Points

C

D

BA

P

DCBA

Collinear Points are points on the same line.

are points that lie in the same plane.

D

C

B

A

Non-collinear points

are points that do not lie on 1 line.

H

G

FE

D

CB

A

Non-coplanar points

are points that do not lieOn 1 plane.

Point A is on line 1.

L1

A

Point A is in line 1.

Line 1 contains point A.

Line 1 is through point A.

L2L1

A

The intersection of line 1 and line2 is point A.

Intersection means the elements in both sets.

Is the symbol for intersection.

Which is in? L2

L1

Which is thru?

L1

L2

In? Under? Above?

L3

L2

L1

L1 L2L3

Which plane containsPoint A ?Point B ?Point C ?Point D ?Line AB ?

DC

B

A

H

V

Both

Both

Both

HV

Classroom Ex. P. 7 1-10Y

X

W

ST

O

R

M

Classroom Ex. P. 7 11-20

D C

HB

A

G

FE

Complete ShapesHow many planes are drawn?

Add Lines to complete the diagram.

How many planes are drawn?6

Complete 3-D diagrams

Number of Planes = 7

Number of Planes = 8

Name the segment that go through point V.

V

T

SR

WName the rest of thePlanes.

VRS

VWTVWR

VST

RST

V

T

SR

W

Complete the

pyramid.

Alternative Plane Drawings

F

ED

CB

A

Note that the intersection of two planes is a line.

AD�������������� �

Therefore, segment AD stretches out to be a line.A real planes goes on for ever.

The boundaries of the planes are only in the model.

G

A

B

C

DE

F

Name the back plane.

Name the left plane.

Name the bottom plane.

Name the top plane.

Name the front plane.

BCF

CDE

ABC

ABG

ADE

H

RL

B

AA

B

A

A

Three planes can intersect at a 1 line.

G

A

B

C

DE

F

Three planes can intersect at a 1 point.

G

FE

D

C

H

RL

B

AA

B

A

A

Point C is in plane _____

Point D is in plane _____

Point E is in plane _____

Point F is in plane _____

Point G is in plane _____

Point A is in plane _____

Point B is in plane _____

H

R

L

H

L

L, R, H

L, R, H

MS

W

O

T

R

Y

X

XY�������������� �

True or False

Intersects plane M at point O.

True

#1

Plane M intersects at more than 1 point.

MS

W

O

T

R

Y

X

XY�������������� �

True or False

False

#2

MS

W

O

T

R

Y

XTrue or False

T, O and R are collinear.

False

#3

MS

W

O

T

R

Y

XTrue or False

X, O, and Y are collinear.

True

#4

MS

W

O

T

R

Y

XTrue or False

R, O, S, and W are coplanar.

True

#5

MS

W

O

T

R

Y

XTrue or False

R, S, T, and X are coplanar.

False

#6

MS

W

O

T

R

Y

XTrue or False

R, X, O and Y are coplanar.

True

#7

MS

W

O

T

R

Y

X

Does a plane have edges?

No

#8

MS

W

O

T

R

Y

X

Can a given point be in 2 lines? Ten lines?

Yes

#9

Yes

MS

W

O

T

R

Y

X

Can a given line be in 2 planes? In 10 planes?

Yes

#10

Yes

Find the fourth point of the plane.

A, B, C, ___

False

#11-16

H G

FE

D C

BA

B, G, C, ___B, E, F, ___A, D, E, ___

D, C, H, ___E, F, H, ___D G G

H A F

H G

FE

D C

BA

Are there any points in line CG besides C and G?

Are there more than 4 points in plane ABCD?

Yes

Yes

H G

FE

D C

BA

Name the intersection of plane ABFE and BCGF.

Name two planes that do not intersect.

BF�������������� �

ABCD & DFGH ABFE & DCGH ADHE & BCGF

C’est fini.

The End