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# Point, Line, Plane - PowerPoint PPT Presentation

Point, Line, Plane. Geometry Terms. Undefined terms: words that do not have a formal definition but there is agreement about what they mean. Defined terms: Terms that can be described using known words Postulate or Axiom: Rule that is accepted without proof.

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Point, Line, Plane

• Undefined terms: words that do not have a formal definition but there is agreement about what they mean.

• Defined terms: Terms that can be described using known words

• Postulate or Axiom: Rule that is accepted without proof.

• Theorem: Rule that can be proved.

Point, Line, Plane

• 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

A

C

Point, Line, Plane

• 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 -

n

A

B

C

Point, Line, Plane

• 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

Collinear

C

A

B

Non collinear

Lesson 1-1 Point, Line, Plane

• 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

M

B

C

Horizontal Plane

Vertical Plane

Other

Lesson 1-1 Point, Line, Plane

A

B

Plane ABCD

Plane EFGH

Plane BCGF

Plane ADHE

Plane ABFE

Plane CDHG

Etc.

D

C

E

F

H

G

Lesson 1-1 Point, Line, Plane

Any three non collinear points determine a plane!

Plane AFGD

Plane ACGE

Plane ACH

Plane AGF

Plane BDG

Etc.

Lesson 1-1 Point, Line, Plane

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

Are the following points coplanar?

A, B, C ?

Yes

A, B, C, F ?

No

H, G, F, E ?

Yes

E, H, C, B ?

Yes

A, G, F ?

Yes

C, B, F, H ?

No

Lesson 1-1 Point, Line, Plane

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

Line m and line n intersect at point P.

P

n

Continued…….

Lesson 1-1 Point, Line, 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

B

P

A

R

Plane P and Plane R intersect at the line

Lesson 1-1 Point, Line, Plane

A is between R and Y.

( the symbol RA is read as “ray RA” )

Ray

Definition:

How to sketch:

How to name:

Lesson 1-2: Segments and Rays

Definition:

If A is between X and Y, AX and AY are opposite rays.

( Opposite rays must have the same “endpoint” )

opposite rays

not opposite rays

Lesson 1-2: Segments and Rays

Part of a line that consists of two points called the endpoints and all points between them.

Definition:

How to sketch:

How to name:

AB (without a symbol) means the length of the segment or the distance between points A and B.

Lesson 1-2: Segments and Rays

AC + CB = AB

x + 2x = 12

3x = 12

x = 4

The Segment Addition Postulate

Postulate:

If C is between A and B, then AC + CB = AB.

If AC = x , CB = 2x and AB = 12, then, find x, AC and CB.

Example:

2x

x

Step 1: Draw a figure

Step 2: Label fig. with given info.

Step 3: Write an equation

x = 4

AC = 4

CB = 8

Step 4: Solve and find all the answers

Lesson 1-2: Segments and Rays

• Pg. 5 # 1

• Pg 6 # 17, 18, 20

• Pg 12 # 8, 10, 12

• Pg 13 #21 to 26, 29

Lesson 1-2: Formulas