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

*click on the content to continue..*

What is a rhombus?

- A parallelogram with all sides equal
- A parallelogram with all sides equal
- not a parallelogram

The answer is "A parallelogram with all sides equal"

A quadrilateral is defined by `5` parameters. A parallelogram is defined by `3` parameters. And in a rhombus, the following properties provide additional dependency of parameters

• All sides are equal (and parallel)

• the diagonals perpendicularly bisect

• opposite angles are equal

• adjacent angles are supplementary These properties cause one parameter dependent on other parameters and effectively, *a rhombus is defined by `2` parameters*.

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

- Consider this as two SSS triangles `ABC` and `ACD`
- Consider this as two SSS triangles `ABC` and `ACD`
- Consider this as an SAS triangle `ABC` and another SSS triangle `BAD`

The answer is "Consider this as two SSS triangles `ABC` and `ACD`"

To construct a rhombus, a side (`bar(AB)`) and an angle (`/_B`) are given. This is illustrated in the figure Which of the following helps to construct the specified rhombus?

- With a side and an angle, a rhombus cannot be constructed
- Consider this as two SAS triangles `ABC` and `BAD`
- Consider this as two SAS triangles `ABC` and `BAD`

The answer is "Consider this as two SAS triangles `ABC` and `BAD`". Use the property `/_A + /_B = 180^@` to find the second angle.

To construct a rhombus, two diagonals (`bar(AC)`, `bar(BD)`) are given. This is illustrated in the figure Which of the following helps to construct the specified rhombus?

- With the two diagonals, a rhombus cannot be constructed
- Consider this as two SAS triangles `DOC` and `AOB` with diagonals perpendicularly bisecting
- Consider this as two SAS triangles `DOC` and `AOB` with diagonals perpendicularly bisecting

The answer is "Consider this as two SAS triangles `DOC` and `AOB`". Use the property that the diagonals perpendicularly bisect and mark the vertices at half diagonals.

**Construction of Rhombus** :

Properties of Rhombus

• All sides are equal (and parallel)

• the diagonals perpendicularly bisect

• opposite angles are equal

• adjacent angles are supplementary The formulations of questions

• `1` side and `1` diagonal

• `1` side and `1` angle

• `2` diagonals *use properties to figure out dependent parameters and look for triangles.*

*slide-show version coming soon*