Introduction to Geometry – Points, Lines, and Planes

Points - have no height or width- represented using a dot and labeled using a capital letter

A

B

C

D

Introduction to Geometry – Points, Lines, and Planes

Points - have no height or width- represented using a dot and labeled using a capital letter

A

B

C

D

Line - has no thickness. Its only dimension is length.

- has no endpoints. It extends forever in each direction. ( arrows )

- it is ALWAYS straight

- labeled with a lower case script letter ( line a )

- if there are points on the line, you can

also name it using the points. ( line AB )

- the part of the line between A and B

is called a line segment

- line segments have definite endpoints

a

A

B

AB

A

B

Introduction to Geometry – Points, Lines, and Planes

Collinear - points that are on the SAME line - a line is really a collection of points - points A, B, and C are collinear

AB

C

Introduction to Geometry – Points, Lines, and Planes

Collinear - points that are on the SAME line - a line is really a collection of points - points A, B, and C are collinear - points D, E, and F are also collinear

AB

C

D

E

F

Introduction to Geometry – Points, Lines, and Planes

Collinear - points that are on the SAME line - a line is really a collection of points - points A, B, and C are collinear - points D, E, and F are also collinear - points A and F are non-collinear

AB

C

D

E

F

Introduction to Geometry – Points, Lines, and Planes

Collinear - points that are on the SAME line - a line is really a collection of points - points A, B, and C are collinear - points D, E, and F are also collinear - points A and F are non-collinear - points B, E, and F are non-collinear

AB

C

D

E

F

Introduction to Geometry – Points, Lines, and Planes

Collinear - points that are on the SAME line - a line is really a collection of points - points A, B, and C are collinear - points D, E, and F are also collinear - points A and F are non-collinear - points B, E, and F are non-collinear

AB

C

D

E

F

Ray – starts at a fixed point and continues in one direction forever

Introduction to Geometry – Points, Lines, and Planes

Collinear - points that are on the SAME line - a line is really a collection of points - points A, B, and C are collinear - points D, E, and F are also collinear - points A and F are non-collinear - points B, E, and F are non-collinear

AB

C

D

E

F

Ray - starts at a fixed point and continues in one direction forever

- named from their starting point and one other point on the ray

( ray AC or )

A

C

AC

Introduction to Geometry – Points, Lines, and Planes

Collinear - points that are on the SAME line - a line is really a collection of points - points A, B, and C are collinear - points D, E, and F are also collinear - points A and F are non-collinear - points B, E, and F are non-collinear

AB

C

D

E

F

Ray - starts at a fixed point and continues in one direction forever

- named from their starting point and one other point on the ray

( ray AC or )

- two rays connected at the same starting point create an angle

A

C

AC

Introduction to Geometry – Points, Lines, and Planes

Geometric plane – a flat surface that has height and width. No thickness.

Introduction to Geometry – Points, Lines, and Planes

Geometric plane - a flat surface that has height and width. No thickness.

- it is two – dimensional and extends in all directions into infinity

- named with capital script letters ( plane K )

K

Introduction to Geometry – Points, Lines, and Planes

Geometric plane - a flat surface that has height and width. No thickness.

- it is two – dimensional and extends in all directions into infinity

- named with capital script letters ( plane K )

- also can be named using three points NOT on the same line

( plane DEF )

DE

F

Introduction to Geometry – Points, Lines, and Planes

Geometric plane - a flat surface that has height and width. No thickness.

- it is two – dimensional and extends in all directions into infinity

- named with capital script letters ( plane K )

- also can be named using three points NOT on the same line

( plane DEF )

DE F

K

C

B

A

H

I

Points lie on planes and are in planes.

Introduction to Geometry – Points, Lines, and Planes

Geometric plane - a flat surface that has height and width. No thickness.

- it is two – dimensional and extends in all directions into infinity

- named with capital script letters ( plane K )

- also can be named using three points NOT on the same line

( plane DEF )

DE F

K

C

B

A

H

I

Points lie on planes and are in planes.

Lines contain points and are in planes

Introduction to Geometry – Points, Lines, and Planes

Geometric plane - a flat surface that has height and width. No thickness.

- it is two – dimensional and extends in all directions into infinity

- named with capital script letters ( plane K )

- also can be named using three points NOT on the same line

( plane DEF )

DE F

K

C

B

A

H

I

Points lie on planes and are in planes.

Lines contain points and are in planes

Planes contain points and lines

Introduction to Geometry – Points, Lines, and Planes

Planes exist in three – dimensional space and contain their own points and lines.

In geometry, you can have multiple planes. ( Planes A and B )

AC

B

ED

F

A

B

Introduction to Geometry – Points, Lines, and Planes

Planes exist in three – dimensional space and contain their own points and lines.

In geometry, you can have multiple planes. ( Planes A and B )

Line AB is in plane A but not in plane B.

AC

B

ED

F

A

B

Introduction to Geometry – Points, Lines, and Planes

Planes exist in three – dimensional space and contain their own points and lines.

In geometry, you can have multiple planes. ( Planes A and B )

Line AB is in plane A but not in plane B.

Point F is in plane B but not in plane A.

AC

B

ED

F

A

B

Introduction to Geometry – Points, Lines, and Planes

Planes exist in three – dimensional space and contain their own points and lines.

In geometry, you can have multiple planes. ( Planes A and B )

Line AB is in plane A but not in plane B.

Point F is in plane B but not in plane A.

Points or lines that lie in the same plane are called coplanar

AC

B

ED

F

A

B

Introduction to Geometry – Points, Lines, and Planes

Here is an example of points and lines that DO NOT lie in plane A.

A CB

E

DF

A

Introduction to Geometry – Points, Lines, and Planes

Here is an example of points and lines that DO NOT lie in plane A.

Points F, D and E are not in plane A.

AB

E

DF

A

C

Introduction to Geometry – Points, Lines, and Planes

Here is an example of points and lines that DO NOT lie in plane A.

Points F, D and E are not in plane A.

Line DE is not in plane A.

AB

E

DF

A

C

Introduction to Geometry – Points, Lines, and Planes

Here is an example of points and lines that DO NOT lie in plane A.

Points F, D and E are not in plane A.

Line DE is not in plane A.

Lines intersect planes they are not contained in at exactly one point ( point C )

AB

E

DF

A

C

Introduction to Geometry – Points, Lines, and Planes

Line Postulate – for any two points, there is exactly one line containing them.

A

B

- a straight line is the shortest distance between two points.

Introduction to Geometry – Points, Lines, and Planes

Line Postulate – for any two points, there is exactly one line containing them.

A

B

- a straight line is the shortest distance between two points.

Theorem – if two lines intersect, they intersect at exactly one point.

E

Introduction to Geometry – Points, Lines, and Planes

Term Dimensions Must Contain

Line One 2 points

Plane Two 3 or more non collinear points

Space Three 4 or more noncoplanar points

Introduction To Geometry – Intersecting Lines and Planes

In geometry you have :

- lines intersecting lines

Introduction To Geometry – Intersecting Lines and Planes

In geometry you have :

- lines intersecting lines

- planes intersecting planes

- lines intersecting planes

Introduction To Geometry – Intersecting Lines and Planes

Postulate – if two planes intersect, their intersection

forms a line.

Postulate – a line not contained in a plane will intersect that plane at exactly one point

C

Introduction To Geometry – Intersecting Lines and Planes

A line in a plane divides the plane into two half – planes.

half – plane

half – plane

a

Introduction To Geometry – Intersecting Lines and Planes

A line in a plane divides the plane into two half – planes.

half – plane

half – plane

aPoints A and B lie in the same half – plane.

AB