1.2 Points, Lines and Planes

1.2 Points,

Lines and Planes

There are three __________ ____________ in geometry.

The following are not definitions, they are descriptions.

undefined terms

•1 A ______________ is the simplest figure studied in geometry. It doesn’t have any size. It is represented by a dot.

point

All geometric figures consist of points. Below are points A, B and C. We name points

with capital letters.A

BC

•2 A ________ extends in two

directions without ending.

It has no thickness.

line

A line is referred to by a single lower case letter (line l ) or using two points on the line (AB or BA).

B

A

l

•3 A __________ is suggested by a floor, wall or table top. However, it exists without ending and has no thickness.

plane

•We use a parallelogram to represent a plane. We label a plane with a capital letter.

M N

Plane M and Plane N.

•We use the three undefined terms to define other concepts.

DCBA

•_________ _________ are points that lie on the same line.

Points A, B, C are collinear. Points A, B and D are noncollinear.

Collinear points

•___________ _________ points are points that lie on the same plane.

• M, N, P, R are coplanar.• M, N, P, Q are noncoplanar.

MN

R

P

Q

Coplanar points

The ____________of two figures is the set of points that are in

both figures.

intersection

Pt

m

Lines m and t intersect at point W.

W

Point P is on line t.

•k and P are in M.•M contains k and P•j intersects M at P.•P is the intersection of j and M.

Pk

M

j

M

N

Y

X

Planes M and N intesect in line XY.

•Ex 1. Using the figure given, list three sets of collinear points.

•Ex 2. List a set of noncollinear points.

AB

C

D

EF

G

A, B, C

F, E, B

A, E, G

A, E, CF, E, C orA, B, D or

M

O

T

WR

S

X

Y

Ex 3. Copy this figure into your notebooks and then answer the T/F questions.

• A) Line XY intersects M at point O.

• B) Plane M intersects line XY in more than one point.

• C) T, O, and R are collinear.• D) X, O, and Y are collinear.• E) R, O, S, and W are coplanar.• F) R, S, T, and X are coplanar.• G) R, X, O and Y are coplanar.

T

F

F

T

T

F

T

• Ex 4. Name a fourth point that is in the same plane as the given points.

• a) A, B, C• b) D, C, H• c) B, E, F• d) D, B, F

D

E

A

H

C

G

F

B

•The plane that contains the top of the box• can be called plane ABCD. (Go around in order)

D

GAH

A. Are there more than 4 points in plane ABCD?

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

C. Name the intersection of planes ABFE and BCGF.

D. Name two planes that do not intersect.

Ex 5.

Yes!! Yes!

!BFABBBBBBBBBBBBB B

ABCD and EFGH

ADHE and BCGF ABFE and DCGH

____________________ consists of points A and C and all points that

are between A and C.

•A and C are called the _____________ of segment AC.

Segment AC

endpoints

A C

AC or CA

__________________ consists of the initial point A and all the

points on line AC that lie on the same side of A as point C.

Ray AC

Name the endpoint first.

A C AC not CABBBBBBBBBBBBBBBBBBBBBBBBBBBB

R S T

Ex 6. Write 3 times when the hands of the clock are opposite rays.

SR and ST are called opposite rays if S is

between R and T

BBBBBBBBBBBBBBBBBBBBBBBBBBBB

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