POINTS LINES AND PLANES,OH MY!

Points, Lines and Planes are the building blocks to understanding

Geometry

Take a line sheet of paper and fold it in three lengthwise, so the paper makes long tall columns.

Label the top of the first column TERMS

Label the top of the second column MEANING

Label the top of the third column REPRESENTATION

In the first column write the word POINT and its meaning in your own words.

In the second column write instructions on how to name a point.

In the third column draw a picture representation of a point and label.

Do the same for the terms LINE and PLANE.

Term meaning or definition figure representation

Cornell NotesWe will be doing these Cornell Notes for your vocabulary words and postulates for the rest of the chapter, and through the rest of the book. It is a great study guide for you now and for the end of course exam.

Term meaning or definition figure representationPoint a point

indicates location and has no size

You can represent a point with a dot and name it with a capital leter such as A.

Line a line is

represented by a straight path that extends in tow opposite directions without end and has no thickness. A line contains infinitely many points.

You can name a line by any two points on the line, such as (read 'line AB') or , or by a single

lowercase letter such as line l

Plane a plane is

represented by a flat surface that extends without end and has no thickness. A plane contains infinitely many lines.

you can name a plane by a capital letter, such as plane P, or by at least three points in the plane that do not all lie on the same line, such as plane ABC

This is about what your Cornell Notes should look like for the first three terms.

1.) Name the points on line m.

2.) Give two other names for line m.

3.) Name a plane that contains line m.

Pt G, Pt J and Pt H

Line GJ, Line JH, line GH

plane N, plane GJK, plane KJH, plane GHK, any combination of three of the points that are not in a straight line.

G

H

J

K

mN

Collinear points are points that lie on the same line

Coplanar points are non-collinear points that lie in the same plane.

Add these to your Cornell notes

1.) Name a set of collinear points.

RQ, RS, TQ, NQ, VR, VS, VT, VN, RT, more!

2.) Name a set of coplanar points.

RVS, TSR, NSR, TNS, QTN TNR, QNS, and more!

Can you see the planes represented by the names above?

Naming a Figure in a Plane

When naming a figure in a plane such as the TOP of the cube given we always pick one corner and read around the figure corner to corner.

A

HG

F

E

DC

BThe top would be named ABCD, or BADC, but NOT ADBCName the bottom and right side of this box. Bottom: GFEH, EHGF, or othersRight DAEH, HEAD, or others

Can you name a plane that is not represented with drawn lines? Plane CHEB is a diagonal plane that runs diagonally

through the box. Can you find more?

A segment is part of a line that consists of two endpoints and all of the points between them.

RS

A ray is part of a line that consists of one endpoint and all the points of the line on one side of the endpoint.

FT NOT TF

Opposite rays are two rays that share the same endpoint and form a line.

RS

F

T

B

A M

AB and AM are opposite rays BA and MA are not

Naming Segments and Rays

Name the segments in line m.

WG, GP, PN, GN, WP, WN,

Name two rays on line m.

GW, GP, GN, PN, PW, NP and more

Name a pair of opposite rays on line m.

GN and GP, or PW and PN

(remember GP and GN are the same ray, as are PW and PG)

mW

G

N

p

An Axiom or a Postulate is a statement of fact. They are statements that, like undefined terms, we believe to be true without proof.

Postulate: Through any two points there is exactly one line.

A

B

How many lines can we draw through A and B?

Only one straight line.

Postulate: If two distinct lines intersect, then they intersect in exactly one point.

Line AE and Line DB intersect at point C

Postulate: If two distinct planes intersect, then they intersect in exactly one line.

Plane RST and Plane STW intersect in line ST.

Postulate: Through any three noncollinear points there is exactly one plane.

Points Q, R, and S are noncollinear. Plane P is the only plane that contains them.

Plane P could also be called Plane QRS

.AD

B

FC

T

1.) Name Plane T in as many ways as you can. ABC, ACD, AFB, ACB, AFD, DBA, DBC, DBF, but NOT ACF as they lie on the same line.

2.) How many lines can be drawn through the given points? Name them.

AC, AD, AB CD, DB, FD, and FB