Lesson 1-1 Point, Line, Plane 1

Lesson 1-3

Point, Line, Plane

Lesson 1-1 Point, Line, Plane 2

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

Lesson 1-1 Point, Line, Plane 3

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

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nA

BC

ABC�������������� �

Lesson 1-1 Point, Line, Plane 4

Collinear Points 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.Ex: To find if A (1, 0) is collinear with

the points on the line y = -3x + 3.

Substitute x = 1 and y = 0 in the equation.

0 = -3 (1) + 3

0 = -3 + 3

0 = 0

The point A satisfies the equation, therefore the point is collinear

with the points on the line.

A B C

AB

C

Collinear

Non collinear

Lesson 1-1 Point, Line, Plane 5

Planes

A plane is a flat surface that extends indefinitely in all directions. 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

Lesson 1-1 Point, Line, Plane 6

Different planes in a figure:A B

CD

EF

GH

Plane ABCD

Plane EFGH

Plane BCGF

Plane ADHE

Plane ABFE

Plane CDHG

Etc.

Lesson 1-1 Point, Line, Plane 7

Other planes in the same figure:

Any three non collinear points determine a plane!

H

E

G

DC

BA

F

Plane AFGD

Plane ACGE

Plane ACH

Plane AGF

Plane BDG

Etc.

Lesson 1-1 Point, Line, Plane 8

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 ?

YesNo

YesYesYesNo

Lesson 1-1 Point, Line, Plane 9

Intersection of Figures

The intersection of two figures is the set of points that are common in both figures.

The intersection of two lines is a point.

m

n

P

Continued…….

Line m and line n intersect at point P.

Lesson 1-1 Point, Line, Plane 10

3 Possibilities of Intersection of a Line and a Plane

(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

Intersection of Two Planes is a Line.

P

R

A

B

Plane P and Plane R intersect at the line AB�������������� �

Lesson 1-1 Point, Line, Plane 12

Postulate or Axiom

A postulate or axiom is an accepted statement as fact.

Postulate and Axioms have no formal proof they exist or are true

Many mathematicians do years of research trying to prove postulates or axioms true.

Postulates and axioms that are proven true are known as Theorems.

Lesson 1-1 Point, Line, Plane 13

Postulate 1-1 Through any two points there is exactly

one line.

Line t is the only line that passes through points A and B.

Lesson 1-1 Point, Line, Plane 14

Postulate 1-2

If two lines intersect they intersect in exactly one point

and intersect at C. AE BD

Lesson 1-1 Point, Line, Plane 15

Postulate 1-3

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

Plane RST and Plane STW Intersect in .

AE

AE

ST

Lesson 1-1 Point, Line, Plane 16

Postulate 1-4

Through any three noncollinear points there is exactly one plane.

“Think of a tripod”