maths > construction-basics

Fundamental Elements of Practical Geometry

    what you'll learn...


The four fundamental elements of Practical Geometry are explained.

  1. Constructing co-linear points.

  2. Constructing equi-distant points

  3. Constructing equi-angular points

  4. Constructing parallel points.

Constructing a Line

constructing a line

A ruler helps to construct a line through two points.

collinear points

The points on a line are called "collinear points".

The word "collinear" means: of lying in the same line.

"co" means "together; jointly" ; and "linear" means "line".


constructing a line

Constructing a Line through two Points: Connect two points using a ruler or a scale and extend in both the directions.

Constructing an Arc

constructing an arc

A "compass" helps to construct an arc at a distance 55cm from point AA.

equidistant points

The points on an arc are called "equidistant points".

The word "equidistant" means: at equal distance.

The points PP, BB, QQ, and RR are at the equal distant from the point AA.


constructing an arc

Constructing an arc : Measure the distance using a compass and mark the arc at the distance from the point.

Constructing an Angle

angle with protractor

A protractor helps to mark an angle of a given measure.

equiangular points

The points on the ray at an angle to ¯AB are called equiangular points to the line.

The word "equiangular" means: having equal angle.


angle with protractor

Constructing a given Angle : Using a protractor measure the given angle and extend the ray.

Constructing a Parallel to a given line

constructing a parallel

Set-squares or set-triangles help to construct a parallel to a given line.

The word "parallel" means: lines having same distance continuously between them.


Constructing a Parallel : Set a leg of the set-square on a line and slide the set-square along its diagonal. The parallel can be constructed on the leg.

fundamental elements

In practical geometry, we study about constructing

  • line segments,

  • angles

that make different plane-figures like triangles, rectangles, quadrilaterals, etc. The following are the fundamental elements to practical geometry.

   constructing a line (collinear points),

   Constructing an arc (equidistant points),

   Constructing an angle or (equiangular points), and

   Constructing a parallel (parallel points)

The fundamental elements of practical geometry are

  1. constructing a straight line using a ruler (which are points collinear to two points).

  2. measuring a distance using a compass and marking an arc (which are points equidistant to the center).

  3. measuring an angle using a protractor and marking a ray with the angle (which are points equiangular to the initial point)

  4. constructing a parallel using set squares (which are points on a line parallel to a given line)

In the course of the lessons, the secondary elements and the end-applications will be explained. For example, bisecting a line or constructing a parallel line using a compass are some examples of secondary elements. The primary elements are used to construct the secondary elements.

And, constructing a square using the length of a diagonal or constructing a parallelogram are some examples of end-applications. These constructions use combination of primary and secondary elements.


Fundamental Elements of Practical Geometry :

  1. Constructing a line connecting 2 points using a scale or ruler: Constructing co-linear points.

  2. Constructing an arc of given radius with a compass : Constructing equi-distant points

  3. Constructing an angle of given measure with a protractor : Constructing equi-angular points

  4. Constructing a parallel at a given distance to a line : Constructing parallel points.


The outline of material to learn "Construction / Practical Geometry at 6-8th Grade level" is as follows. Note: click here for detailed outline of "constructions / practical geometry".

  •   Four Fundamenatl elements

    →   Geometrical Instruments

    →   Practical Geometry Fundamentals

  •   Basic Shapes

    →   Copying Line and Circle

  •   Basic Consustruction

    →   Construction of Perpendicular Bisector

    →   Construction of Standard Angles

    →   Construction of Triangles

  •   Quadrilateral Forms

    →   Understanding Quadrilaterals

    →   Construction of Quadrilaterals

    →   Construction of Parallelograms

    →   Construction of Rhombus

    →   Construction of Trapezium

    →   Construction of Kite

    →   Construction of Rectangle

    →   Construction of Square