Construction / Practical Geometry (basics) : Construction of Trapezium

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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 $4$ $4$

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

Understanding Trapezium

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

Quadrilateral is defined by $5$ $5$ 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 $4$ $4$ parameters.

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

To construct a trapezium, $2$ $2$ bases ( $¯ ¯¯¯¯ ¯ A B$ $bar(AB)$ , $¯ ¯¯¯¯ ¯ C D$ $bar(CD)$ ) , $1$ diagonal ( $bar(AC)$ ) and $1$ side ( $bar(BC)$ ) 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 ( $bar(AB)$ , $bar(CD)$ ), $1$ side ( $bar(BC)$ ), 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 ( $bar(AB)$ , $bar(CD)$ ), a diagonal ( $bar(AC)$ ), 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( $bar(AB)$ ), a diagonal ( $bar(AC)$ ), 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