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

In this page, a short and to-the-point overview of constructing rectangles is provided. It is outlined as follows.

• Properties of rectangles is explained

• The number of independent parameters in a rectangle is `1`

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

*click on the content to continue..*

What is a rectangle?

- a parallelogram with all interior angles `90^@`
- a parallelogram with all interior angles `90^@`
- a rectangle is not a parallelogram

The answer is "a parallelogram with all interior angles `90^@`"

A quadrilateral is defined by `5` parameters. A Parallelogram is defined by `3` parameters. And for a rectangle, the following properties provide additional dependency of parameters.

• all interior angles are `90^@`

• diagonals are equal and bisect

• opposite sides are parallel and equal

• two angles on diagonals are supplementary These properties cause one parameter to be dependent on other parameters and so, *a rectangle is defined by `2` parameters*.

To construct a rectangle, `2` sides (`bar(AB)`, `bar(BC)`) are given. This is illustrated in the figure. Which of the following helps to construct the specified rectangle?

- Consider this as two SAS triangles `ABC` and `BAD`
- Consider this as two SAS triangles `ABC` and `BAD`
- Consider this as two RHS triangles `ABC` and `ACD`

The answer is "Consider this as two SAS triangles `ABC` and `ABD`".

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

- Consider this as two SAS triangles `ABC` and `BAD`
- Consider this as two RHS triangles `ABC` and `ACD`
- Consider this as two RHS triangles `ABC` and `ACD`

The answer is "Consider this as two RHS triangles `ABC` and `ABD`".

To construct a rectangle, the diagonal (`bar(AC)`) and the angle between them (`/_DOC`) are given. This is illustrated in the figure. Which of the following helps to construct the specified rectangle?

- Consider this as two SAS triangles `COD` and `AOB`
- Consider this as two RHS triangles `ABC` and `ABD`
- Consider this as two RHS triangles `ABC` and `ABD`

The answer is "Consider this as two SAS triangle `COD` and `AOB`". Note: Use the property that diagonals bisect and mark the vertices at half diagonals.

**Construction of Rectangles** :

Properties of rectangle

• all interior angles are `90^@`

• diagonals are equal and bisect

• opposite sides are parallel and equal The formulations of questions

• `2` sides

• `1` side and the diagonal

• the diagonal and an angle between the diagonals *use properties to figure out dependent parameters and look for triangles*

*slide-show version coming soon*