1.2 points, lines, planes.ppt

Warm-Up: Common Words

• What are “common words” we use in

• everyday conversation?

• Do you have to think about their

• meaning?

• What if you didn’t know these words?

• In today’s lesson you will learn about

• common words needed to speak the

• language of geometry

What is a definition?What is a definition?• Known words used to describe a new Known words used to describe a new

wordword

Undefined termsUndefined terms – not formally defined – not formally defined

There are 3 in geometry.There are 3 in geometry.

PointPoint LineLine PlanePlane

Segments, rays, and angles are defined in terms of these basic figures.

Points, Lines, & PlanesPoints, Lines, & PlanesObjectives

Students will be able to:• Define: Point, line, plane, collinear, coplanar, line segment, ray• Name collinear and coplanar points• Draw lines, line segments, and rays with proper labeling

Example what your note page should look like now

Points, Lines, & PlanesPoints, Lines, & Planes August 16, 2010August 16, 2010

Objectives:• Define: Point, line, plane, collinear, coplanar, line

segment, ray• Name collinear and coplanar points• Draw lines, line segments, and rays with proper

labeling

PointPoint

1. Has no dimension (no length, width, 1. Has no dimension (no length, width, thickness)thickness)

2. Usually represented by a dot2. Usually represented by a dot

3. Named using one capital letter3. Named using one capital letter

• BB

6

Points

• Points do not have actual size.

• How to Sketch:

Using dots

• How to label:

Use capital letters

Never name two points with the same letter (in the same sketch).

A

B AC

LineLine1.1. Extends forever in one dimension (length)Extends forever in one dimension (length)

2.2. Has an arrowhead on each end Has an arrowhead on each end representing the fact that it goes on representing the fact that it goes on foreverforever

3.3. Consists of an infinite amount of pointsConsists of an infinite amount of points

4.4. Always straightAlways straight

AA BB

ll

Lesson 1-1 Point, Line, Plane 8

Lines

• Lines extend indefinitely and have no thickness or width.• How to sketch : using arrows at both ends.

• How to name: 2 ways(1) small script letter – line n(2) any two points on the line -

• Never name a line using three points - , , , , ,AB BC AC BA CA CB

������������������������������������������������������������������������������������������������������������������������������������������������ �����������

nA

BC

ABC�������������� �

PlanePlane

1.1. Extends forever in 2 dimensions (length & Extends forever in 2 dimensions (length & width)width)

2.2. A flat surface consisting of infinitely many A flat surface consisting of infinitely many pointspoints

3.3. Usually represented by a 4-sided figureUsually represented by a 4-sided figure

AA

BC

W

10

Planes

• How to sketch: Use a parallelogram (four sided figure)

• How to name: 2 ways

(1) Capital script letter – Plane M(2) Any 3 non collinear points in the plane - Plane: ABC/ ACB / BAC /

BCA / CAB / CBA

A

BC

Horizontal Plane

M

Vertical Plane Other

11

Different planes in a figure:

A B

CD

EF

GH

Plane ABCD

Plane EFGH

Plane BCGF

Plane ADHE

Plane ABFE

Plane CDHG

Etc.

More DefinitionsMore Definitions

• Collinear points –Collinear points –

points that lie on the same points that lie on the same lineline

• Coplanar points – Coplanar points –

points that lie on the same planepoints that lie on the same plane

Practice : Naming Points

• Name a point that is collinear with the given points

• B and E:• C and H:• D and G:• A and C:• H and E:• G and B:

• Name a point that is coplanar with the given points

• M, N, R:• M, N, O:• M, T, Q:• Q, T, R:• T, R, S:• Q, S, O:

Lesson 1-1 Point, Line, Plane 15

Coplanar Objects

Coplanar objects (points, lines, etc.) are objects that lie on the same plane. The plane does not have to be visible.

H

E

G

DC

BA

F

Are the following points coplanar?

A, B, C ?

A, B, C, F ?

H, G, F, E ?

E, H, C, B ?

A, G, F ?

C, B, F, H ?

Yes

No

Yes

Yes

Yes

No

Line SegmentLine Segment (or segment) (or segment)

• A section of a line that has 2 endpointsA section of a line that has 2 endpoints

• Named by its endpoints. AB or BANamed by its endpoints. AB or BA

AA BB

RayRay• Piece of a line with only one endpoint Piece of a line with only one endpoint

(initial point) and continues forever in the (initial point) and continues forever in the other directionother direction

• Named by the endpoint and a second point Named by the endpoint and a second point named on the ray. (name MUST begin with named on the ray. (name MUST begin with the endpoint!)the endpoint!)

ABAB

AABB

Opposite RaysOpposite Rays

• 2 rays that share a common initial point 2 rays that share a common initial point and face opposite directions. and face opposite directions.

• QP and QS are opposite rays.QP and QS are opposite rays.

PP QQ SS

A. Name 4 points in the figure.

B. Name the two lines in the figure.

C. Name the plane in the figure.

D. Name four segments in the figure.

E. Name four rays in the figure.

Two or more geometric intersect if they

have one or more points in common.

• Lines k and l have point A in common, so point A is the intersection • Two planes

intersect in a line

Modeling Activity

Activity Questions

1. When the cards are NOT together:

What is the intersection of AB and CD? AB and EF?

2. With the cards together, what is the intersection of CD and EF?

3. What is the intersection of planes M and N?

4. Are CD and EF coplanar? Explain.

Assignment

General: Worksheet 1.2AGeneral: Worksheet 1.2AHonors: Worksheet 1.2BHonors: Worksheet 1.2B