Relationships Among Points, Lines and Planes

Relationships Among Points, Lines and Planes

By Kleven Lucksly Quijon

Undefined Terms​

In Geometry, there are basic teachnical terms that are defined and undefined.

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An undefined terms is a word a term which does not require any further explanantion or elaborate description. It is a word already in its basic form which you can illustrate by giving concrete examples.​

Undefined Terms​

Undefined terms are used to define or explain more complex terms or concepts.

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In geometry, undefined terms are the basic concepts upon which other statements are built.​

Undefined Terms​

Points, lines and planes are undefined terms in Geometry.​

Point​

A point refers to the idea of an exact fixed location.

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It has no size and dimension.​

Points are represented by dots using capital letters.​

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Point​

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Models/Representation

tip of a pencil, corner of the box, dot in a sheet of paper.​

Open Ended

Give one example of an object modeled or represented by a point.

Line

​A line is a set of infinitely many points arranged in a straight path which extends endlessly in opposite directions.

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It has infinite length but no width nor thickness.​

A line is represented by double arrows and named by using two points on the line or by a single small letter.

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A​ line is named by placing

​the symbol ↔ above the letters.

Line ​

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Models/Representations

tightly-stretched string, edge of the table, edge of a bix, a crease of folded paper, horizon​

Multiple Choice

Which of the following is a correct figure of a line?

Open Ended

Give an example of a an object that can be represented/modeled by a line

Plane

A plane is a flat surface that extends endlessly in all directions.

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It has infinite length and width but not thickness.​

A plane is represented by a four-sided figure.

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A plane is named by using three points on the plane which do not lie on the same line or by a script capital letter.​

Plane​

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Model/Representation

a piece of paper, surface of a floor an artist's canvass​

Open Ended

Give one way in naming the plane.

Identify the undefined term represented by the following objects​

Multiple Choice

tip of a needle

• Point

• Line

• Plane

Multiple Choice

a wall

• Point

• Line

• Plane

Multiple Choice

string of a guitar

• Point

• Line

• Plane

Multiple Choice

a star in the sky

• Point

• Line

• Plane

Multiple Choice

top of the box

• Point

• Line

• Plane

Multiple Choice

clothesline

• Point

• Line

• Plane

Multiple Choice

a mole

• Point

• Line

• Plane

Postulate​

Postulates are statements that are accepted as true without proof.

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They are usually stated using undefined terms and definitions​

Every line contains atleast two points.​

​Postulate 1.2

Two points are cointained in exactly one line

​Postulate 1.1

Postulates of Undefined terms

​Postulates 1.1 and 1.2 imply that two points determine a line and that line has infinite number of points.

Collinear points are points that lie on the same line.

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Otherwise, they are non-collinear points​

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​Collinear points

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Multiple Choice

A, B and E are collinear points

• True

• False

Multiple Choice

P, X, Q are collinear points

• True

• False

If two points are in a plane, then the line containing these two points is also in the plane​

​Postulate 1.3

Postulates of Undefined Terms

​Postulate 1.3 means that points A and B are in Plane M, then line AB is also in plane M

Every plane contains at least three non collinear points.

​Postulate 1.4

Postulates of Undefined Terms

​Postulate 1.4 tells us that three non-collinear points A, B, C determine plane M

Coplanar Points are points that lie on the same plane, other wise they are non coplanar points

​Coplanar Points

Points that do not belong on the same plane.​

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Ex​

A and E are non-coplnar points​

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​Non-coplanar Points

Multiple Choice

J and L are coplanar points

• True

• False

Multiple Choice

A and B are non coplanar points

• True

• False

If two planes intersect, their intersection is a point or a lline​

Postulate 1.6

In space, there exists at least four non coplnar points

​Postulate 1.5

Postulates of Undefined Terms

If a line and a plane intersect, their intersection is either a point or a line

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Plane P and Q intersect at line m

Multiple Choice

Plane q and l intersect at line CD

• True

• False