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Construction of Trapezium


    what you'll learn...

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.

trapezium introduction

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.

construction of trapezium with 2 bases, 1 diagonal, 1 side

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.

construction of trapezium with 2 bases, 1 side, and an angle

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

construction of trapezium with 2 bases, 1 diagonal, and an angle

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.

construction of trapezium with 1 base, 1 diagonal, and 2 angle

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

trapezium introduction

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