Mathematical System in Geometry

Mathematics

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​3rd Quarter

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Sir Lenard A. Soriano

Teacher I​​i

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Review : What Am I?

Direction : Determine whether each of the following represents a Point, Line or Plane.

Multiple Choice

Stars in the sky a night

• Point

• Line

• Plane

Multiple Choice

Piece of rope

• Point

• Line

• Plane

Multiple Choice

Top of table

• Point

• Line

• Plane

Multiple Choice

Edge of a book

• Point

• Line

• Plane

Multiple Choice

Grains of Sand

• Point

• Line

• Plane

Open Ended

How I’m going to visualize terminologies in geometry since many of them are abstract?

Mathematical System in Geometry

Quarter 3 Module 1

Sir Lenard A. Soriano

Undefined Terms

They don’t have definite or exact definitions but can only be described using simpler known terms.

Undefined Terms

Words that don't require a formal definition.​​

It is considered to be true ​without having to be proved or formally defined.

Defined terms

Terms that have a formal definition and can be defined using other geometric terms.

Example of Undefined terms

• Point

• Line 

• Plane

Undefined terms : Point

• A point does not occupy an area

• It does not have any width, length or depth

• A single capital letter is used to name a point.

Undefined terms : Point

Point A

⋅A

Example: Point

tip phillips screwdriver

Example : Point

Grain of Rice

Multiple Choice

Which of the following represent a point?

Multiple Choice

What is the name of the term?

• Point d

• Point D

• d

Undefined terms : Line

• A collection of continuous points that extends indefinitely in either direction

Undefined terms : Line

• It does not have any width

• To name a line, use two points on the line with a line over the two letters or a small script letter.

Undefined terms : Line

• Line VN

• Line NV

• line m

Example: Line

the horizon between a sky and sea

Example: Line

pipette

Multiple Choice

Which of the following represent a line?

Multiple Choice

What is the name of the term?

• Line B

• Line A

• line d

Undefined terms : Plane

• A set of points contained in a flat surface and extends indefinitely in all directions

Undefined terms : Plane

• A plane is commonly denoted as a closed four-sided figure

Undefined terms : Plane

• A plane is named by putting a capital letter on one of the corners.

To name a Plane

• Capital Script letter

• 3 non- collinear points on the plane

Example : Plane

top tools box

Example : Plane

Microscope slide

Defined terms

Terms that have a formal definition and can be defined using other geometric terms.

Example of defined terms

• Collinear Points and Non-collinear Points

• Coplanar Points and non-coplanar points

Defined terms : Collinear Points

are points that lie on the same line

Example : Collinear

Points H, D and C

Defined terms : Non-collinear Points

are points that do not on the same line.

Example : Non-collinear Points

Points L, N and D are non-collinear.

Example of defined terms

• Collinear Points and Non-collinear Points

• Coplanar Points and non-coplanar points

Defined terms : Coplanar Points

are points that lie on the same plane,

Defined terms : Non-Coplanar points

are points that do not lie on the same plane.

Example : Coplanar Points and Non-Coplanar points

Points R, T and Y are coplanar. While Q, R, Y and T are non-coplanar.

Multiple Choice

TRUE or False : Points A, N and D are collinear

• TRUE

• FALSE

Multiple Choice

TRUE or FALSE : Points M, K , R and T are Coplanar

• TRUE

• FALSE

What I Have Learned

Reflect on the topic and activities you have done this day by completing the following statements.

Open Ended

I learned about

Open Ended

2 out of 4 mathematical system

Open Ended

Undefined Vs Defined terms

Open Ended

3 Example of Undefined terms

Open Ended

Real Life Examples: Point

Open Ended

Real Life Examples: Line

Open Ended

Real Life Examples: Plane

Open Ended

Example of defined terms