Construction of Trapezium

overview

In this page, constructing trapezium is explained. It is outlined as follows.

• Properties of trapezium is explained

• The number of independent parameters in a trapezium is 44

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

Understanding Trapezium

A trapezium is a quadrilateral with one pair of parallel sides.

Quadrilateral is defined by 55 parameters. In a trapezium, the following property provides dependence of parameters

• one pair of sides are parallel

Note: The sides that are parallel are called bases. The other two sides are referred as sides.*A trapezium is defined by 44 parameters*.

To construct a trapezium, 22 bases (¯AB¯¯¯¯¯¯AB, ¯CD¯¯¯¯¯¯CD) , 1 diagonal (¯AC) and 1 side (¯BC) are given. This is illustrated in the figure. To construct, consider as an SSS triangle in ABC and mark D on a parallel.

To construct a trapezium, 2 bases (¯AB, ¯CD), 1 side (¯BC), and an angle (∠B) are given. This is illustrated in the figure. To construct, consider this as a SAS triangle in ABC and mark D on a parallel

To construct a trapezium, 2 bases (¯AB, ¯CD), a diagonal (¯AC), and the angle between diagonal and the base (∠CAB)are given. This is illustrated in the figure. To construct, consider this as a SAS triangle in CAB and mark D on a parallel.

To construct a trapezium, a base(¯AB), a diagonal (¯AC), and 2 angles (∠A, ∠B) on the given base are given. This is illustrated in the figure. To construct, consider this as a SAS triangle in ABC and construct ray AD to mark D on a parallel

summary

**Construction of Trapezium** :

Properties of trapezium:

• one pair of sides are parallel

Note: The sides that are parallel are called bases. The other two sides are referred as sides.

The formulations of questions

• 2 bases, 1 side, 1 diagonal

• 2 bases, 1 diagonal, 1 angle between one base and the given diagonal

• 2 bases, 1 side, 1 angle between one base and given side

• 1 base, 2 angles on the given base, 1 diagonal
*use properties to figure out dependent parameters and look for triangles.*

Outline

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__