Plane Geometry

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Objective:

To investigate the influence of the study of geometry to the present-day generations.

The word "geometry" was derived from Greek words "geo" for earth and "metron" for measure. It is all about points, lines, planes, angles and solids. Like any other fields of mathematics, geometry is based on undefined elements, assumed relations, postulates, assumptions, and theorems. These gave rise to different geometries. At least 5000 years ago, Egyptian surveyors used geometry to reestablish field boundaries which were wased out by the annual flooding of Nile river.

Terms associated with Plane Geometry

I. Point

A point is the simplest of all geometric figures. It has no dimension. It is represented by a dot, which is not a geometric point but a physical point.

Mathematicians use capital letters of the English alphabet to name points.

Illustration:

•A is read as "point A."

•C is read as "point C."

Collinear points are points that fall in one line.

Illustration:

Coplanar points are points that belong to one plane.

Illustration:

Points A, M, P, and C are collinear.

Points A, P, and K are noncollinear.

Points B, X, S, and Y are coplanar.

Points B, X, H, and R are noncoplanar.

II. Line

A line, like a point, is considered as an undefined term. It can be represented but can be described only in relation to other geometric elements. Euclid determined that one, and only one line can pass through two distinct points. Below is a physical representation of a line with points A, B, C, and D on the line.

The arrows on both ends signify that the line is infinite -- has immeasurable length.

Hence space is a set of all points, we might as well say that line is a set of collinear points joined together.

Naming a line

A line can be named by any two points on the line or by a symbol written near the arrow's end.

The line above can be named as:

;line AB or line BA

;line AC or line CA

;line BD or line DB

;line AD or line DA

;line p

SUBSETS of a LINE

 1.) line segment

A line segment is a subset of a line with two endpoints. It has a definite length.

 2.) ray

A ray is a subset of a line with one endpoint and points to one direction.

segment PS or segment SP.

ray SP

segment XY or segment YX

ray XY

Part 2 will be posted tomorrow. Stay tuned!

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