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

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

• Properties of kites is explained

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

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

*click on the content to continue..*

What is a kite?

- a quadrilateral with two pairs of equal and adjacent sides
- a quadrilateral with two pairs of equal and adjacent sides
- kite is not a quadrilateral

The answer is "a quadrilateral with two pair of equal and adjacent sides"

A quadrilateral is defined by `5` parameters. For a kite, the following properties provide additional dependency of parameters

• two pair of equal sides

• major diagonal perpendicularly bisects the minor diagonal. *the diagonal that divides the kite into two congruent triangles is called major. The other diagonal is the minor diagonal.*

• major diagonal bisects the angles at the vertices

• two equal opposite angles and two unequal opposite angles -- all sum up to `360^@` *A kite is defined by `3` parameters*.

To construct a kite, `2` unequal sides (`bar(AB)`, `bar(BC)`) and the angle between them (`/_B`) are given. This is illustrated in the figure Which of the following helps to construct the specified kite?

- Consider as an SAS triangle in `BAD` and an SSS triangle `BCD`
- Consider as an SAS triangle in `BAD` and an SSS triangle `BCD`
- Consider as two ASA triangles in `BAD` and `BCD`

The answer is "Consider as an SAS triangle in `BAD` and SSS triangle `BCD`"

To construct a kite, a side (`bar(AB)`) and `2` angles (`/_A`,`/_B`) are given. This is illustrated in the figure Which of the following helps to construct the specified kite?

- Consider as an SAS triangle in `ABC` and an ASA triangle `ACD`
- Consider as an SAS triangle in `ABC` and an ASA triangle `ACD`
- Consider as two ASA triangles in `ABC` and `ACD`

The answer is "Consider as an SAS triangle in `ABC` and ASA triangle `ACD`"

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

- Consider as two SSS triangles in `ABD` and `BDC`
- Consider as two SSS triangles in `ABD` and `BDC`
- Consider as two ASA triangles in `BAD` and `BCD`

The answer is "Consider as two SSS triangles in `ABD` and `BDC`"

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

- Consider as two isosceles SSS triangles in `ABC` and `ACD`
- Consider as two isosceles SSS triangles in `ABC` and `ACD`
- Consider as two ASA triangles in `BAD` and `BCD`

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

To construct a kite, a side (`bar(AB)`), the major diagonal (`bar(BD)`), and angle (`/_ABD`) between them are given. This is illustrated in the figure Which of the following helps to construct the specified kite?

- Consider as two SSS triangles in `ABC` and `ACD`
- Consider as two SAS triangles in `ABD` and `DBC`
- Consider as two SAS triangles in `ABD` and `DBC`

The answer is "Consider as two SAS triangles in `ABD` and `DBC`"

**Construction of Kite** :

Properties of Kite:

• two pair of equal sides

• major diagonal perpendicularly bisects the minor diagonal. *The diagonal that divides the kite as two congruent triangles is the major diagonal.*

• major diagonal bisects the angles at the vertices

• two equal opposite angles and two unequal opposite angles sum up to `360^@` The formulations of questions

• `2` unequal sides and the angle between them

• `1` side and `2` angles

• `2` unequal sides and the major diagonal

• `2` unequal sides and the minor diagonal

• `1` side, major diagonal and the angle between them

*slide-show version coming soon*