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first page of notes. All tests until the Regents are open notes, so don’t miss any. [OTCQ questions ] Your answer . . . . Date 9/9/09 Aim Hwk p 1.1 What is an undefined term? How 1.1 What is an undefined term? How do we define a set, point, line do we define a set, point, line and plane? and plane? [Continue with ppt notes and [Continue with ppt notes and examples] examples] [Expect 5-10 pages of notes every [Expect 5-10 pages of notes every day, min] day, min]

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[OTCQ questions ] Your answer. Date 9/9/09. Aim Hwk p. 1.1 What is an undefined term? How do we define a set, point, line and plane? [Continue with ppt notes and examples] [Expect 5-10 pages of notes every day, min]. - PowerPoint PPT Presentation

### Transcript of [OTCQ questions ] Your answer . . . .

OTCQ: Write this as your first page of notes. All tests until the Regents are open notes, so don’t miss any.

[OTCQ questions ]

Date

9/9/09

Aim

Hwk p

1.1 What is an undefined term? How do we 1.1 What is an undefined term? How do we define a set, point, line and plane? define a set, point, line and plane?

[Continue with ppt notes and examples][Continue with ppt notes and examples][Expect 5-10 pages of notes every day, min][Expect 5-10 pages of notes every day, min]

Aim 1.1 What is an Undefined Term? How do we define a Set, Point, Line and Plane?Homework read chapter 1-1complete problems 3-11 on page 3.rreidymath.wikispaces.com is my website. All in class powerpoints are posted there so that your notebook may always be up to date.

OBJECTIVES

• SWBAT to define an undefined term.

• SWBAT differentiate an undefined terms from a defined term.

• SWBAT sketch pictures that represent defined terms and undefined terms.

[do not write]NYS Performance Indicatorsfor 1.1Students will use the language of mathematics to express mathematical ideas precisely.

G.CM.10 Use correct mathematical language in developing mathematical questions that elicit, extend, or challenge other students’ conjectures

G.CM.12 Draw conclusions about mathematical ideas through decoding, comprehension, and interpretation of mathematical visuals, symbols, and technical writing

What is an undefined term?

In Geometry there are 4 undefined terms

set,

point,

line

plane.

set, point, line & plane

the undefined terms

We say these are undefined because we need to assume their meanings in order to use them to define other things.

Undefined terms

Meanings are assumedAt the start of geometry

Defined terms

Meanings are based on the Undefined terms.

Vs.

set, point, line & plane

the undefined terms

Compare geometry to a game.

Can you explain how rules have to be agreed on up front so that a game may begin?

Definitions of the Undefined terms

SET: A set is a collection of objects defined so that it is possible to say whether an item is in the set or not.

Example: The Yankees are a set.

Derek Jeter was in this set in 2009.

Jose Reyes was not in this set in 2009.

Definitions of the Undefined terms

Point:

A point indicates a location. A point has no width or dimension.

A point is usually represented by a small dot.

A

Point A

Line:

A line is a set of points. A line may be curved or straight.

A straight line includes two arrowheads to indicate that the line extends without end in two directions.

A

B

l

Line l or AB

Definitions of the Undefined terms

Plane:

A plane is a set of points that form a flat surface that extends infinitely in two dimensions.

A plane usually represented by a shape that looks like a tabletop or wall.

A plane extends without end even though the drawing of a plane appears to have edges.

A

BC

M

Plane M or plane ABC

Definitions of the Undefined terms

Next: defined terms. (ie terms based on the undefined terms )• Collinear points are points that lie on the

same line.

• Coplanar points are points that lie on the same plane.

Ex. 1: Naming Collinear and Coplanar Pointsa. Name three points

that are collinear

Solution:

D, E and F lie on the same line, so they are collinear.

G

D E F

H

Ex. 1: Naming Collinear and Coplanar Pointsb. Name four points that

are coplanar.

Solution:

D, E, F, and G lie on the same plane, so they are coplanar. Also D, E, F, and H are coplanar; although, the plane containing them is not drawn.

G

D E F

H

Ex. 1: Naming Collinear and Coplanar Pointsc. Name three points

that are not collinear.

Solution: There are many correct

answers. For instance, points H, E, and G do not lie on the same line.

G

D E F

H

• The line segment or segment AB (symbolized by AB) consists of the endpoints A and B, and all points on AB that are between A and B. Line AB

A

A

B

B

Line segment AB

Next: line segment vs. line

More . . .

• The ray AB (symbolized by AB) consists of the initial point A and all points on AB that lie in the same direction from A as point B.

l

Line l or AB

A

A

B

B

Ray AB

More . . .

• Note that AB is the same as BA and AB is the same as BA. However, AB and BA are not the same. They have different initial points and extend in different directions.

l

Line l or AB

A

A

B

B

Ray BA

More . . . • If C is between A and B,

then CA and CB are opposite rays.

• Like points, segments and rays are collinear if they lie on the same line. So, any two opposite rays are collinear. Segments, rays and lines are coplanar if they lie on the same plane.

l

Line l or AB

A

C

B

Ex. 2: Drawing lines, segments and rays

• Draw three noncollinear points J, K, and L.

Then draw JK, KL and LJ.

J

K

L

Draw J, K and L

Then draw JK

Ex. 2: Drawing lines, segments and rays

• Draw three noncollinear points J, K, and L.

Then draw JK, KL and LJ.

J

K

L

Draw KL

Ex. 2: Drawing lines, segments and rays

• Draw three noncollinear points J, K, and L.

Then draw JK, KL and LJ.

J

K

L

Draw LJ

Ex. 3: Drawing Opposite Rays

• Draw two lines. Label points on the lines and name two pairs of opposite rays.

Solution: Points M, N, and

X are collinear and X is

between M and N. So

XM and XN are opposite

rays.

P

MQ

N

X

Ex. 3: Drawing Opposite Rays

• Draw two lines. Label points on the lines and name two pairs of opposite rays.

Solution: Points P, Q, and

X are collinear and X is

between P and Q. So XP

and XQ are opposite

rays.

P

MQ

N

X

Ex. 4: Sketching intersection of a plane and a line.• Sketch the figure

described.a. A line that intersects a

plane in one point Draw a plane and a

line. Emphasize the point

where they meet. Dashes indicate

where the line is hidden by the plane

Ex. 4: Sketching intersection of 2 planes.• Sketch the figure

described.

b. Two planes that intersect in a line

Draw two planes. Emphasize the line

where they meet. Dashes indicate where

one plane is hidden by the other plane.

View Homework p.3 problems 3- 11

• The Geometry text is available at

www.harborfieldscsd.net/

And

http://www.harborfieldscsd.net/pdf/HS/textbook/Geometry.pdf

ALL HOMEWORK GOES IN THE BACK OF YOUR NOTEBOOK!