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We will try to answer:

1. What are the undefined terms in geometry?

2. What concepts present the foundations of geometry?

3. Can you sketch the intersection of lines and planes?

1. What are the undefined terms in geometry?

2. What concepts present the foundations of geometry?

3. Can you sketch the intersection of lines and planes?

1.
Basics of Geometry

Basics of Geometry

POINTS!

LINES!

PLANES!

OH MY!

Basics of Geometry

POINTS!

LINES!

PLANES!

OH MY!

2.
Basics of Geometry

• What are the undefined terms in geometry?

• What concepts present the foundations of

geometry?

• Can you sketch the intersection of lines and

planes?

These questions (and much more!!) will be

answered by the end of this presentation.

Are you ready?

• What are the undefined terms in geometry?

• What concepts present the foundations of

geometry?

• Can you sketch the intersection of lines and

planes?

These questions (and much more!!) will be

answered by the end of this presentation.

Are you ready?

3.
Basics of Geometry

Undefined Terms?

The terms points, lines, and planes are the foundations of

geometry, but…

point, line, and plane are all what we call undefined terms.

How can that be?

Well, any definition we could give them would depend on the

definition of some other mathematical idea that these three

terms help define. In other words, the definition would be

Undefined Terms?

The terms points, lines, and planes are the foundations of

geometry, but…

point, line, and plane are all what we call undefined terms.

How can that be?

Well, any definition we could give them would depend on the

definition of some other mathematical idea that these three

terms help define. In other words, the definition would be

4.
Basics of Geometry

Point

• Has no dimension

• Usually represented by a small dot

A

The above is called point A. Note the point

is represented with a capital letter.

Point

• Has no dimension

• Usually represented by a small dot

A

The above is called point A. Note the point

is represented with a capital letter.

5.
Basics of Geometry

Line

• Extend in one dimension.

• Represented with straight line with two arrowheads to

indicate that the line extends without end in two directions.

l This is Line l, (using the lower case

script letter) or symbolically we call it AB

A

B NOTICE: The arrowheads are in

both directions on the symbol AB

Line

• Extend in one dimension.

• Represented with straight line with two arrowheads to

indicate that the line extends without end in two directions.

l This is Line l, (using the lower case

script letter) or symbolically we call it AB

A

B NOTICE: The arrowheads are in

both directions on the symbol AB

6.
Basics of Geometry

Plane

• Extend in two dimensions.

• Represented by a slanted 4 sided figure, but you must

envision it extends without end, even though the

representation has edges.

A M This is Plane M or plane ABC (be

C sure to only use three of the

B points when naming a plane)

Plane

• Extend in two dimensions.

• Represented by a slanted 4 sided figure, but you must

envision it extends without end, even though the

representation has edges.

A M This is Plane M or plane ABC (be

C sure to only use three of the

B points when naming a plane)

7.
Basics of Geometry

Undefined Concepts

• Collinear points are points that lie on the

same line.

l

A

B Points A, B and C are collinear.

C

Undefined Concepts

• Collinear points are points that lie on the

same line.

l

A

B Points A, B and C are collinear.

C

8.
Basics of Geometry

Undefined Concepts

• Coplanar points are points that lie on the

same plane.

A

C Points A, B and C are coplanar.

B

Undefined Concepts

• Coplanar points are points that lie on the

same plane.

A

C Points A, B and C are coplanar.

B

9.
Basics of Geometry

Line Segment

Let’s look at the idea of a point in between two other points on a line.

Here is line AB, or recall A B

symbolically AB

The line segment does not

extend without end. It has

endpoints, in this case A and

B. The segment contains all

the points on the line

between A and B

This is segment AB

Notice the difference in

the symbolic notation!

Line Segment

Let’s look at the idea of a point in between two other points on a line.

Here is line AB, or recall A B

symbolically AB

The line segment does not

extend without end. It has

endpoints, in this case A and

B. The segment contains all

the points on the line

between A and B

This is segment AB

Notice the difference in

the symbolic notation!

10.
Basics of Geometry

Let’s look at a ray:

A is called the initial

point The initial point is

always the first

A B letter in naming a

ray. Notice the

difference in

Ray AB extends in symbols from both

one direction a line and segment.

without end.

Symbolized by AB

Let’s look at a ray:

A is called the initial

point The initial point is

always the first

A B letter in naming a

ray. Notice the

difference in

Ray AB extends in symbols from both

one direction a line and segment.

without end.

Symbolized by AB

11.
Basics of Geometry

Symbol alert!

Not all symbols are created equal!

AB is the same as BA A B

AB is the same as BA A B

BUT…

Symbol alert!

Not all symbols are created equal!

AB is the same as BA A B

AB is the same as BA A B

BUT…

12.
Basics of Geometry

Symbol alert!!

The ray is different! Initial point 1st

AB is not the same as BA

A B AB

A B BA

Notice that the initial point is listed first in the symbol. Also

note that the symbolic ray always has the arrowhead on the right

regardless of the direction of the ray.

Symbol alert!!

The ray is different! Initial point 1st

AB is not the same as BA

A B AB

A B BA

Notice that the initial point is listed first in the symbol. Also

note that the symbolic ray always has the arrowhead on the right

regardless of the direction of the ray.

13.
Basics of Geometry

Opposite Rays

If C is between A and B,

A C B

then CA and CB are opposite rays.

C is the common initial point for the rays!

Opposite Rays

If C is between A and B,

A C B

then CA and CB are opposite rays.

C is the common initial point for the rays!

14.
Basics of Geometry

Angles

Rays are important because they help us define something very

important in geometry…Angles!

An angle consists of two different rays that have the same initial

point. The rays are sides of the angles. The initial point is called the

vertex. Notation: We denote an angle with

three points and symbol. The

vertex B middle point is always the vertex.

We can also name the angle with

sides just the vertex point. This angle can

A be denoted as:

C BAC , CAB, or A

Angles

Rays are important because they help us define something very

important in geometry…Angles!

An angle consists of two different rays that have the same initial

point. The rays are sides of the angles. The initial point is called the

vertex. Notation: We denote an angle with

three points and symbol. The

vertex B middle point is always the vertex.

We can also name the angle with

sides just the vertex point. This angle can

A be denoted as:

C BAC , CAB, or A

15.
Basics of Geometry

Classifying Angles

Angles are classified as acute, right, obtuse, and straight,

according to their measures. Angles have measures greater

than 0° and less or equal to 180°.

A A A A

Acute angle Right angle Obtuse angle Straight angle

0°< m A < 90° m A = 90° 90°< m A < 180° m A = 180°

Classifying Angles

Angles are classified as acute, right, obtuse, and straight,

according to their measures. Angles have measures greater

than 0° and less or equal to 180°.

A A A A

Acute angle Right angle Obtuse angle Straight angle

0°< m A < 90° m A = 90° 90°< m A < 180° m A = 180°

16.
Basics of Geometry

Intersections of lines and planes

• Two or more geometric figures intersect if they have

one or more points in common.

• The intersection of the figures is the set of points the

figure has in common

Think How do 2 line intersect?

!! How do 2 planes intersect?

What about a line and a plane?

Intersections of lines and planes

• Two or more geometric figures intersect if they have

one or more points in common.

• The intersection of the figures is the set of points the

figure has in common

Think How do 2 line intersect?

!! How do 2 planes intersect?

What about a line and a plane?

17.
Basics of Geometry

Modeling Intersections

To think about the questions on the last slide lets look at the following…

Point E is

Two lines E the

intersect at a intersection

point, like here of plane H

A F and line EC

at point A. B

D

H C

G

Line BF is the intersection of the

planes G and H.

Modeling Intersections

To think about the questions on the last slide lets look at the following…

Point E is

Two lines E the

intersect at a intersection

point, like here of plane H

A F and line EC

at point A. B

D

H C

G

Line BF is the intersection of the

planes G and H.

18.
Basics of Geometry

Something to think about…

You have just finished the first section in Geometry!

This is a very important section because it lays the foundation for

the rest of the year! Much of the vocabulary you will encounter in

this course will have its foundation in the ideas presented in this

lesson.

Can you name the three undefined terms in geometry? Do

you know the difference between and obtuse and straight angle?

Can you sketch the intersection of a plane and a line? How about

two planes? Can you visualize the intersection of two planes? How

about three?

The classfun and homefun provided will help you in developing a

better understanding of the concepts!

Something to think about…

You have just finished the first section in Geometry!

This is a very important section because it lays the foundation for

the rest of the year! Much of the vocabulary you will encounter in

this course will have its foundation in the ideas presented in this

lesson.

Can you name the three undefined terms in geometry? Do

you know the difference between and obtuse and straight angle?

Can you sketch the intersection of a plane and a line? How about

two planes? Can you visualize the intersection of two planes? How

about three?

The classfun and homefun provided will help you in developing a

better understanding of the concepts!