geometry

geometry

By Meneo Salvar

UNDEFINED TERMS

By Meneo Salvar

Point, Line, Plane

By Meneo Salvar

Point

​žcan be represented by a dot.

ž it has zero dimension because it has no length, width or depth/height.

žIt is an exact position on a plane or in space.

žObjects like a tip of a needle, the tip of a pencil, a corner of a sheet of paper, etc.

By Meneo Salvar

Line

žmay be represented by a straight segment.

ž it has dimension 1 because it has length but no width nor depth.

žis an infinite set of points arranged in an array. It extends infinitely in opposite directions.

žObjects like the edge of a table,or the path of a moving object model a line.

Note: Any two points determine a line.

By Meneo Salvar

Line

žNaming a Line:​

A line can be named using two capital letters with a double arrowhead above them or a lower case letter.

​

     AB,   BA , or m

Read: Line AB

           Line BA

           Line m

By Meneo Salvar

Plane

žž is usually modeled by a sheet of paper.

ž  is 2-dimensional because it has length and width, but no depth.

žIt extends infinitely in all directions.

žlike Physical objects table top,blackboard,etc. model a plane.

žAny three non-collinear points determine a plane.

By Meneo Salvar

Naming a Plane:By using a single

capital letter

Read : Plane M 

By Meneo Salvar

M​

Space

ž is usually referred to as the collection of all points.

žIt is 3-dimensional because it has length, width and depth.

ž it has no end and extends infinitely in all directions​

By Meneo Salvar

Example: Identify the undefined term represented by each concrete object.

1. Yarn

2. floor

3. wire

4. button

5. clothesline

6. tip of a syringe

7. edge of a table

8. intersection of front wall, sidewall, and ceiling.

9. Window pane

10. intersection of flagpole and the ground​

By Meneo Salvar

By Meneo Salvar

Quiz: Place each object to its corresponding column in the table below:      

Point	Line	PLane

​

​Cover of a book              Corner of a table                tip of a needle

Sun Rays                        Electric wire                  surface of a table      hole                                 bottle cap                           TV antenna

hairstrand                        shoelace                            Wall 

Edge of a blackboard      bedsheet                            drinking straw

Tip of a guava leaf          stars in the night sky       screen of a laptop

Intersection of ballpen and paper

intersection of the side  wall and ceiling

By Meneo Salvar

​

	Point	Line	PLane
	Tip of a guava leaf Intersection of ballpen and paper Corner of a table Bottle cap Stars in the night sky Tip of a needle	sun rays Hairstrand Edge of a blackboard Intersection of the side wall and ceiling Electric wire Shoelace Tv antenna Drinking straw	cover of a book Bedsheet Surface of a table Wall Screen of a laptop

​Solution

By Meneo Salvar

​6. It is usually referred to as the collection of all points.

7. It is represented by a flat surface.

8. 2 dimensional bec.it has length and width.

9. It is 3-dimensional because it has length, width and depth.

10. It is an exact position on a plane or in space. ​

By Meneo Salvar

​6. It is usually referred to as the collection of all points.

7. It is represented by a flat surface.

8. 2 dimensional bec.it has length and width.

9. It is 3-dimensional because it has length, width and depth.

10. It is an exact position on a plane or in space. ​

By Meneo Salvar

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By Meneo Salvar

​A	​B	C​	D​
​Pencil	hair​	edsa avenue​	blackboard​
top of table​	street​	bangkal street​	table corner​
​tip of pencil	roof​	laptop​	water tube​
​meralco post	corner​	notebook​	tube pipe​
bed sheet​	wall​	table edge​	water hose​
sheet of paper​	floor​	wire​	plate​
star in the sky​	ceiling ​	leaf surface​	finger​
tip of hair​	finger​	road surface​	tip of finger​
rice grain​	finger nail​	bathroom door​	tip of nose ​

By Meneo Salvar

​A	​B
​Point	​bathroom door
line​	​tip of mountain
plane​	​tip of hair
​	falling hair​
​	table top​