__maths__>__Construction / Practical Geometry (basics)__>__Construction of Quadrilaterals__### 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.

*click on the content to continue..*

What is a trapezium?

- A parallelogram with two pairs of parallel sides
- A quadrilateral with one pair of parallel sides
- A quadrilateral with one pair of parallel sides

The answer is "A quadrilateral with one pair of parallel sides"

Quadrilateral is defined by `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` parameters*.

To construct a trapezium, `2` bases (`bar(AB)`, `bar(CD)`) , `1` diagonal (`bar(AC)`) and `1` side (`bar(BC)`) are given. This is illustrated in the figure Which of the following helps to construct the specified trapezium?

- consider as an SSS triangle `ABC` and mark `D` on a parallel
- consider as an SSS triangle `ABC` and mark `D` on a parallel
- consider as an ASA triangle `ABC` and mark `D` on a ray

The answer is "consider as an SSS triangle in `ABC` and mark `D` on a parallel"

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 Which of the following helps to construct the specified trapezium?

- consider as as SAS triangle in `ABC` and mark `D` on a parallel
- consider as as SAS triangle in `ABC` and mark `D` on a parallel
- consider as a ASA triangle in `ABC` and mark `D` on a ray

The answer is "consider as a SAS triangle in `ABC` and mark `D` on a parallel"

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 Which of the following helps to construct the specified trapezium?

- consider as a SAS triangle `CAB` and mark `D` on a parallel
- consider as a SAS triangle `CAB` and mark `D` on a parallel
- consider as a ASA triangle `ABC` and mark `D` on a ray

The answer is "consider as a SAS triangle in `CAB` and mark `D` on a parallel"

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 Which of the following helps to construct the specified trapezium?

- consider as an SSS triangle `ABC`
- consider as an SAS triangle `ABC` and construct ray `AD` to mark `D` on a parallel
- consider as an SAS triangle `ABC` and construct ray `AD` to mark `D` on a parallel

The answer is "consider as a SAS triangle in `ABC` and construct ray `AD` to mark `D` on a parallel"

**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.*

*slide-show version coming soon*