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

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

• Properties of squares is explained

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

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

*click on the content to continue..*

What is a square?

- a rectangle with all sides equal
- a rectangle with all sides equal
- a square is not a rectangle

The answer is "a rectangle with all sides equal"

A rectangle is defined by `2` parameters. And in a square, the following properties provide additional dependency of parameters.

• all sides are equal

• diagonals are equal and perpendicularly bisect

• opposite sides are parallel

• all interior angles are `90^@`

• two angles on diagonals are supplementary These properties cause one parameter to be dependent on other parameters and so, *a square is defined by `1` parameter*.

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

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

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

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

- Mark the vertices at half diagonals on perpendicular lines
- Mark the vertices at half diagonals on perpendicular lines
- Consider this as two RHS triangles `ABC` and `ACD`

The answer is "Consider as two SAS triangles and Mark the vertices at half diagonals on perpendicular lines". Use the property that diagonals bisect.

**Construction of Square** :

Properties of Square:

• all sides are equal

• diagonals are equal and perpendicularly bisect

• opposite sides are parallel

• all interior angles are `90^@` The formulations of questions

• `1` side

• `1` diagonal *use properties to figure out dependent parameters and look for triangles*

*slide-show version coming soon*