Lesson 1-1 Point, Line, Plane 1

Point, Line, Plane

Point – a specific location in space 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).

Lesson 1-1 Point, Line, Plane 2

A

B AC

Line- segment extending forever in opposite directions Lines extend indefinitely and have no thickness or width. How to sketch : using arrows at both ends.

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

Never name a line using three points – 2 points make up a line

, , , , ,AB BC AC BA CA CB#$#$#$#$#$#$$#$#$#$#$#$$#$#$#$#$#$$#$#$#$#$#$$#$#$#$#$#$$#$#$#$#$#$$#$#$#$#$#$$#$#$#$#$#$$#$#$#$#$#$$#$#$#$#$#$$#$#$#$#$#$$#$#$#$#$#$$#$#$#$#$#$ $#$#$#$#$#$

ABC#$$$$$$$$$$$$$ $

Lesson 1-1 Point, Line, Plane 3

n AB

C

Collinear points are points that lie on the same line. (The line does not have to be visible.)

A point lies on the line if the coordinates of the point satisfy the equation of the line.

Lesson 1-1 Point, Line, Plane 4

A B C AB

C

Collinear

Non collinear

A plane is a flat surface that extends indefinitely in all directions. How to sketch: Use a parallelogram (four sided figure) How to name: 3 ways(1) Capital script letter – Plane M, M, Plane ABC(2) Any 3 non collinear points in the plane - Plane: ABC/ ACB / BAC /

BCA / CAB / CBA

Lesson 1-1 Point, Line, Plane 5

A

BC

Horizontal Plane

M

Vertical Plane Other

Lesson 1-1 Point, Line, Plane 6

A B

CD

EF

GH

Plane ABCD

Plane EFGH

Plane BCGF

Plane ADHE

Plane ABFE

Plane CDHG

Etc.

Any three non collinear points determine a plane!

Lesson 1-1 Point, Line, Plane 7

H

E

G

DC

BA

F

Plane AFGD

Plane ACGE

Plane ACH

Plane AGF

Plane BDG

Etc.

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

Lesson 1-1 Point, Line, Plane 8

H

E

G

DC

BA

F

Are the following points coplanar?

A, B, C ?

H, G, F, E ?

E, H, C, B ?A, G, F ?

Yes

Yes

YesYes

Points that could not be connected by a plane are said to be Non Coplanar

pointsA C B FB C E G

Lesson 1-1 Point, Line, Plane 9

H

E

G

DC

BA

F

NO

NO

The intersection of two figures is the list of all points that are shared by both figures.

Lesson 1-1 Point, Line, Plane 10

The intersection of two lines is a point.

m

n

P

Continued…….

Line m and line n intersect at point P.

(1) Line passes through plane – intersection is a point.(2) Line lies on the plane - intersection is a line.(3) Line is parallel to the plane - no common points.

Lesson 1-1 Point, Line, Plane 11

Lesson 1-1 Point, Line, Plane 12

III

III IVORIG

IN

X-Axis

Y-Axis

FOG pg 7-8 #1-5, 8-11,13-15,19-21in workbook

Geometry pg 7-8 #1-5,11-14, 17,18, 20-25, 30-35 in workbook

Lesson 1-1 Point, Line, Plane 13