Construction / Practical Geometry (basics)

Welcome to the only place where practical geometry is explained in an *ingenious and simplified form*.

The geometrical instruments are introduced as *four fundamental elements of practical geometry*

• collinear points (straight-line using a ruler)

• equidistant points (arch using a compass)

• equiangular points (angle using a protractor)

• parallel points (parallel using set-squares)

Based on the four fundamental elements, the topics in practical geometry are explained.

Geometrical Instruments

In this page, overview of the geometrical instruments is provided

• graduated ruler or scale

• compass

• protractor

• divider

• set-squares or set-triangles

Fundamental Elements of Practical Geometry

In this page, the four 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.

Construction of Line, Circle, Angle

In this page, overview of construction of the following are provided

• a line segment

• a circle of given radius

• a semi circle of given radius

• a line by copying another line

• constructing an angle by copying another angle

Perpendicular Bisector to a Line Segment

In this page, the following are explained.

• constructing a bisector to a line segment

• constructing a perpendicular through a point on a line

• constructing a perpendicular to a point not on a line

• constructing a bisector to a given angle

Constructing $60}^{\circ$ angle using Compass

In this page, constructing the following using a compass are explained.

• $60}^{\circ$ angle

• $30}^{\circ$ angle

• $120}^{\circ$ angle

• $15}^{\circ$ angle

• $90}^{\circ$ angle

Fundamentals of Construction : Triangles

This lesson gives a short overview of triangles. Three parameters define a triangle and the following possible combinations uniquely define a triangle

• Side-Side-Side (SSS)

• Side-Angle-Side (SAS)

• Angle-Side-Angle (ASA)

• right angle-hypotenuse-side (RHS)

• side-angle-altitude (SAL)

This set of parameters are given to construct a triangle.

A short analysis of constructing triangles with the following is provided.

• angle-angle-side (equivalent to angle-side-angle)

• angle-angle-angle (only 2 parameters)

• side-side-angle (two possible triangles)

• side-side-altitude (two possible triangles)

• rightangle-angle-side (equivalent to angle-side-angle)

Fundamentals of Construction : Quadrilaterals

In this page, a short overview of approaching construction problems for various quadrilateral forms is provided.

• A quadrilateral form has some additional properties, for example: all sides of a square are equal and the four angles are $90}^{\circ$.

• A quadrilateral is seen to be combination of two triangles.

Using the properties, the construction is simplified into combination of triangles of sss, sas, asa, rhs, sal.

Construction of Quadrilaterals

In this page, a short and to-the-point overview of constructing quadrilaterals is provided. It is outlined as follows.

• Properties of quadrilaterals is explained

• The number of independent parameters in a quadrilateral is $1$

• For a given parameter, construction of quadrilaterals is approached as combination of triangles (sss, sas, asa, rhs, sal) and using the properties of quadrilaterals.

Construction of Parallelograms

In this page, a short and to-the-point overview of constructing parallelograms is provided. It is outlined as follows.

• Properties of parallelograms is explained

• The number of independent parameters in a parallelogram is $3$

• For a given parameter, construction of parallelograms is approached as combination of triangles (sss, sas, asa, rhs, sal) and using the properties of parallelograms.

Construction of Rhombus

In this page, a short and to-the-point overview of constructing rhombus is provided. It is outlined as follows.

• Properties of rhombus is explained

• The number of independent parameters in a rhombus is $2$

• For a given parameter, construction of rhombus is approached as combination of triangles (sss, sas, asa, rhs, sal) and using the properties of rhombus.

Construction of Trapezium

In this page, a short and to-the-point overview of constructing trapezium is provided. It is outlined as follows.

• Properties of trapezium is explained

• The number of independent parameters in a trapezium is $4$

• For a given parameter, construction of trapezium is approached as combination of triangles (sss, sas, asa, rhs, sal) and using the properties of trapezium.

Construction of Kite

In this page, a short and to-the-point overview of constructing kites is provided. It is outlined as follows.

• Properties of kites is explained

• The number of independent parameters in a kite is $1$

• For a given parameter, construction of kites is approached as combination of triangles (sss, sas, asa, rhs, sal) and using the properties of kites.

Construction of Rectangles

In this page, a short and to-the-point overview of constructing rectangles is provided. It is outlined as follows.

• Properties of rectangles is explained

• The number of independent parameters in a rectangle is $1$

• For a given parameter, construction of rectangles is approached as combination of triangles (sss, sas, asa, rhs, sal) and using the properties of rectangles.

Construction of Square

In this page, a short and to-the-point overview of constructing squares is provided. It is outlined as follows.

• Properties of squares is explained

• The number of independent parameters in a square is $1$

• For a given parameter, construction of squares is approached as combination of triangles (sss, sas, asa, rhs, sal) and using the properties of squares.